Basic properties
| Modulus: | \(3236\) | |
| Conductor: | \(3236\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(202\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3236.l
\(\chi_{3236}(7,\cdot)\) \(\chi_{3236}(51,\cdot)\) \(\chi_{3236}(115,\cdot)\) \(\chi_{3236}(207,\cdot)\) \(\chi_{3236}(299,\cdot)\) \(\chi_{3236}(319,\cdot)\) \(\chi_{3236}(343,\cdot)\) \(\chi_{3236}(407,\cdot)\) \(\chi_{3236}(411,\cdot)\) \(\chi_{3236}(435,\cdot)\) \(\chi_{3236}(451,\cdot)\) \(\chi_{3236}(475,\cdot)\) \(\chi_{3236}(527,\cdot)\) \(\chi_{3236}(555,\cdot)\) \(\chi_{3236}(615,\cdot)\) \(\chi_{3236}(623,\cdot)\) \(\chi_{3236}(627,\cdot)\) \(\chi_{3236}(683,\cdot)\) \(\chi_{3236}(687,\cdot)\) \(\chi_{3236}(723,\cdot)\) \(\chi_{3236}(739,\cdot)\) \(\chi_{3236}(783,\cdot)\) \(\chi_{3236}(791,\cdot)\) \(\chi_{3236}(799,\cdot)\) \(\chi_{3236}(855,\cdot)\) \(\chi_{3236}(983,\cdot)\) \(\chi_{3236}(999,\cdot)\) \(\chi_{3236}(1011,\cdot)\) \(\chi_{3236}(1031,\cdot)\) \(\chi_{3236}(1051,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{101})$ |
| Fixed field: | Number field defined by a degree 202 polynomial (not computed) |
Values on generators
\((1619,1621)\) → \((-1,e\left(\frac{97}{101}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3236 }(319, a) \) | \(-1\) | \(1\) | \(e\left(\frac{93}{202}\right)\) | \(e\left(\frac{63}{101}\right)\) | \(e\left(\frac{11}{202}\right)\) | \(e\left(\frac{93}{101}\right)\) | \(e\left(\frac{87}{202}\right)\) | \(e\left(\frac{69}{101}\right)\) | \(e\left(\frac{17}{202}\right)\) | \(e\left(\frac{46}{101}\right)\) | \(e\left(\frac{77}{202}\right)\) | \(e\left(\frac{52}{101}\right)\) |