Basic properties
Modulus: | \(1444\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1444.r
\(\chi_{1444}(65,\cdot)\) \(\chi_{1444}(141,\cdot)\) \(\chi_{1444}(145,\cdot)\) \(\chi_{1444}(217,\cdot)\) \(\chi_{1444}(221,\cdot)\) \(\chi_{1444}(297,\cdot)\) \(\chi_{1444}(369,\cdot)\) \(\chi_{1444}(373,\cdot)\) \(\chi_{1444}(445,\cdot)\) \(\chi_{1444}(449,\cdot)\) \(\chi_{1444}(521,\cdot)\) \(\chi_{1444}(525,\cdot)\) \(\chi_{1444}(597,\cdot)\) \(\chi_{1444}(601,\cdot)\) \(\chi_{1444}(673,\cdot)\) \(\chi_{1444}(677,\cdot)\) \(\chi_{1444}(749,\cdot)\) \(\chi_{1444}(753,\cdot)\) \(\chi_{1444}(825,\cdot)\) \(\chi_{1444}(829,\cdot)\) \(\chi_{1444}(901,\cdot)\) \(\chi_{1444}(905,\cdot)\) \(\chi_{1444}(977,\cdot)\) \(\chi_{1444}(981,\cdot)\) \(\chi_{1444}(1053,\cdot)\) \(\chi_{1444}(1057,\cdot)\) \(\chi_{1444}(1129,\cdot)\) \(\chi_{1444}(1133,\cdot)\) \(\chi_{1444}(1205,\cdot)\) \(\chi_{1444}(1209,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((723,1085)\) → \((1,e\left(\frac{73}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 1444 }(65, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{28}{57}\right)\) |