Basic properties
| Modulus: | \(1444\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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 1444.s
\(\chi_{1444}(7,\cdot)\) \(\chi_{1444}(11,\cdot)\) \(\chi_{1444}(83,\cdot)\) \(\chi_{1444}(87,\cdot)\) \(\chi_{1444}(159,\cdot)\) \(\chi_{1444}(163,\cdot)\) \(\chi_{1444}(235,\cdot)\) \(\chi_{1444}(239,\cdot)\) \(\chi_{1444}(311,\cdot)\) \(\chi_{1444}(315,\cdot)\) \(\chi_{1444}(387,\cdot)\) \(\chi_{1444}(391,\cdot)\) \(\chi_{1444}(463,\cdot)\) \(\chi_{1444}(467,\cdot)\) \(\chi_{1444}(539,\cdot)\) \(\chi_{1444}(543,\cdot)\) \(\chi_{1444}(615,\cdot)\) \(\chi_{1444}(619,\cdot)\) \(\chi_{1444}(691,\cdot)\) \(\chi_{1444}(695,\cdot)\) \(\chi_{1444}(767,\cdot)\) \(\chi_{1444}(771,\cdot)\) \(\chi_{1444}(843,\cdot)\) \(\chi_{1444}(847,\cdot)\) \(\chi_{1444}(919,\cdot)\) \(\chi_{1444}(923,\cdot)\) \(\chi_{1444}(995,\cdot)\) \(\chi_{1444}(999,\cdot)\) \(\chi_{1444}(1071,\cdot)\) \(\chi_{1444}(1075,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((723,1085)\) → \((-1,e\left(\frac{25}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) |