Basic properties
| Modulus: | \(8041\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{473}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.ds
\(\chi_{8041}(35,\cdot)\) \(\chi_{8041}(613,\cdot)\) \(\chi_{8041}(766,\cdot)\) \(\chi_{8041}(919,\cdot)\) \(\chi_{8041}(987,\cdot)\) \(\chi_{8041}(1344,\cdot)\) \(\chi_{8041}(1718,\cdot)\) \(\chi_{8041}(2075,\cdot)\) \(\chi_{8041}(2228,\cdot)\) \(\chi_{8041}(2449,\cdot)\) \(\chi_{8041}(2670,\cdot)\) \(\chi_{8041}(3401,\cdot)\) \(\chi_{8041}(3418,\cdot)\) \(\chi_{8041}(3537,\cdot)\) \(\chi_{8041}(3911,\cdot)\) \(\chi_{8041}(4132,\cdot)\) \(\chi_{8041}(4149,\cdot)\) \(\chi_{8041}(4880,\cdot)\) \(\chi_{8041}(5594,\cdot)\) \(\chi_{8041}(6036,\cdot)\) \(\chi_{8041}(6342,\cdot)\) \(\chi_{8041}(6767,\cdot)\) \(\chi_{8041}(7345,\cdot)\) \(\chi_{8041}(7498,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{7}{10}\right),1,e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 8041 }(2449, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) |