Basic properties
| Modulus: | \(1011\) | |
| Conductor: | \(337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{337}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1011.bl
\(\chi_{1011}(28,\cdot)\) \(\chi_{1011}(91,\cdot)\) \(\chi_{1011}(94,\cdot)\) \(\chi_{1011}(100,\cdot)\) \(\chi_{1011}(112,\cdot)\) \(\chi_{1011}(115,\cdot)\) \(\chi_{1011}(145,\cdot)\) \(\chi_{1011}(190,\cdot)\) \(\chi_{1011}(211,\cdot)\) \(\chi_{1011}(229,\cdot)\) \(\chi_{1011}(259,\cdot)\) \(\chi_{1011}(274,\cdot)\) \(\chi_{1011}(313,\cdot)\) \(\chi_{1011}(325,\cdot)\) \(\chi_{1011}(334,\cdot)\) \(\chi_{1011}(340,\cdot)\) \(\chi_{1011}(349,\cdot)\) \(\chi_{1011}(361,\cdot)\) \(\chi_{1011}(400,\cdot)\) \(\chi_{1011}(415,\cdot)\) \(\chi_{1011}(445,\cdot)\) \(\chi_{1011}(463,\cdot)\) \(\chi_{1011}(484,\cdot)\) \(\chi_{1011}(529,\cdot)\) \(\chi_{1011}(559,\cdot)\) \(\chi_{1011}(562,\cdot)\) \(\chi_{1011}(574,\cdot)\) \(\chi_{1011}(580,\cdot)\) \(\chi_{1011}(583,\cdot)\) \(\chi_{1011}(646,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((338,10)\) → \((1,e\left(\frac{127}{168}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1011 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{127}{168}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) |