Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(198\) | 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 3267.bn
\(\chi_{3267}(23,\cdot)\) \(\chi_{3267}(56,\cdot)\) \(\chi_{3267}(155,\cdot)\) \(\chi_{3267}(221,\cdot)\) \(\chi_{3267}(254,\cdot)\) \(\chi_{3267}(320,\cdot)\) \(\chi_{3267}(353,\cdot)\) \(\chi_{3267}(419,\cdot)\) \(\chi_{3267}(452,\cdot)\) \(\chi_{3267}(518,\cdot)\) \(\chi_{3267}(551,\cdot)\) \(\chi_{3267}(617,\cdot)\) \(\chi_{3267}(650,\cdot)\) \(\chi_{3267}(716,\cdot)\) \(\chi_{3267}(749,\cdot)\) \(\chi_{3267}(815,\cdot)\) \(\chi_{3267}(914,\cdot)\) \(\chi_{3267}(947,\cdot)\) \(\chi_{3267}(1013,\cdot)\) \(\chi_{3267}(1046,\cdot)\) \(\chi_{3267}(1112,\cdot)\) \(\chi_{3267}(1145,\cdot)\) \(\chi_{3267}(1244,\cdot)\) \(\chi_{3267}(1310,\cdot)\) \(\chi_{3267}(1343,\cdot)\) \(\chi_{3267}(1409,\cdot)\) \(\chi_{3267}(1442,\cdot)\) \(\chi_{3267}(1508,\cdot)\) \(\chi_{3267}(1541,\cdot)\) \(\chi_{3267}(1607,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{99})$ |
| Fixed field: | Number field defined by a degree 198 polynomial (not computed) |
Values on generators
\((3026,244)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{198}\right)\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{29}{198}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{16}{99}\right)\) | \(e\left(\frac{95}{198}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{23}{66}\right)\) |