Basic properties
| Modulus: | \(323\) | |
| Conductor: | \(323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | 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 323.ba
\(\chi_{323}(2,\cdot)\) \(\chi_{323}(15,\cdot)\) \(\chi_{323}(32,\cdot)\) \(\chi_{323}(53,\cdot)\) \(\chi_{323}(59,\cdot)\) \(\chi_{323}(60,\cdot)\) \(\chi_{323}(70,\cdot)\) \(\chi_{323}(110,\cdot)\) \(\chi_{323}(117,\cdot)\) \(\chi_{323}(127,\cdot)\) \(\chi_{323}(128,\cdot)\) \(\chi_{323}(155,\cdot)\) \(\chi_{323}(162,\cdot)\) \(\chi_{323}(185,\cdot)\) \(\chi_{323}(212,\cdot)\) \(\chi_{323}(219,\cdot)\) \(\chi_{323}(223,\cdot)\) \(\chi_{323}(230,\cdot)\) \(\chi_{323}(257,\cdot)\) \(\chi_{323}(280,\cdot)\) \(\chi_{323}(281,\cdot)\) \(\chi_{323}(287,\cdot)\) \(\chi_{323}(298,\cdot)\) \(\chi_{323}(314,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((20,154)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 323 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{23}{24}\right)\) |