Basic properties
| Modulus: | \(1011\) | |
| Conductor: | \(337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{337}(332,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1011.bi
\(\chi_{1011}(58,\cdot)\) \(\chi_{1011}(76,\cdot)\) \(\chi_{1011}(88,\cdot)\) \(\chi_{1011}(97,\cdot)\) \(\chi_{1011}(127,\cdot)\) \(\chi_{1011}(136,\cdot)\) \(\chi_{1011}(142,\cdot)\) \(\chi_{1011}(157,\cdot)\) \(\chi_{1011}(178,\cdot)\) \(\chi_{1011}(202,\cdot)\) \(\chi_{1011}(235,\cdot)\) \(\chi_{1011}(268,\cdot)\) \(\chi_{1011}(271,\cdot)\) \(\chi_{1011}(280,\cdot)\) \(\chi_{1011}(394,\cdot)\) \(\chi_{1011}(403,\cdot)\) \(\chi_{1011}(406,\cdot)\) \(\chi_{1011}(439,\cdot)\) \(\chi_{1011}(472,\cdot)\) \(\chi_{1011}(496,\cdot)\) \(\chi_{1011}(517,\cdot)\) \(\chi_{1011}(532,\cdot)\) \(\chi_{1011}(538,\cdot)\) \(\chi_{1011}(547,\cdot)\) \(\chi_{1011}(577,\cdot)\) \(\chi_{1011}(586,\cdot)\) \(\chi_{1011}(598,\cdot)\) \(\chi_{1011}(616,\cdot)\) \(\chi_{1011}(679,\cdot)\) \(\chi_{1011}(685,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((338,10)\) → \((1,e\left(\frac{67}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1011 }(1006, a) \) | \(-1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{83}{112}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{67}{112}\right)\) | \(e\left(\frac{33}{112}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{3}{7}\right)\) |