Basic properties
Modulus: | \(2001\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{667}(382,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bl
\(\chi_{2001}(34,\cdot)\) \(\chi_{2001}(67,\cdot)\) \(\chi_{2001}(109,\cdot)\) \(\chi_{2001}(178,\cdot)\) \(\chi_{2001}(241,\cdot)\) \(\chi_{2001}(274,\cdot)\) \(\chi_{2001}(283,\cdot)\) \(\chi_{2001}(295,\cdot)\) \(\chi_{2001}(352,\cdot)\) \(\chi_{2001}(382,\cdot)\) \(\chi_{2001}(412,\cdot)\) \(\chi_{2001}(448,\cdot)\) \(\chi_{2001}(457,\cdot)\) \(\chi_{2001}(502,\cdot)\) \(\chi_{2001}(526,\cdot)\) \(\chi_{2001}(544,\cdot)\) \(\chi_{2001}(586,\cdot)\) \(\chi_{2001}(589,\cdot)\) \(\chi_{2001}(613,\cdot)\) \(\chi_{2001}(631,\cdot)\) \(\chi_{2001}(700,\cdot)\) \(\chi_{2001}(709,\cdot)\) \(\chi_{2001}(718,\cdot)\) \(\chi_{2001}(730,\cdot)\) \(\chi_{2001}(787,\cdot)\) \(\chi_{2001}(796,\cdot)\) \(\chi_{2001}(847,\cdot)\) \(\chi_{2001}(904,\cdot)\) \(\chi_{2001}(934,\cdot)\) \(\chi_{2001}(937,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((1,e\left(\frac{21}{22}\right),e\left(\frac{11}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(382, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{18}{77}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{20}{77}\right)\) | \(e\left(\frac{60}{77}\right)\) |