Basic properties
Modulus: | \(2001\) | |
Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | 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 2001.bq
\(\chi_{2001}(35,\cdot)\) \(\chi_{2001}(62,\cdot)\) \(\chi_{2001}(71,\cdot)\) \(\chi_{2001}(167,\cdot)\) \(\chi_{2001}(179,\cdot)\) \(\chi_{2001}(209,\cdot)\) \(\chi_{2001}(236,\cdot)\) \(\chi_{2001}(266,\cdot)\) \(\chi_{2001}(353,\cdot)\) \(\chi_{2001}(386,\cdot)\) \(\chi_{2001}(440,\cdot)\) \(\chi_{2001}(473,\cdot)\) \(\chi_{2001}(515,\cdot)\) \(\chi_{2001}(560,\cdot)\) \(\chi_{2001}(584,\cdot)\) \(\chi_{2001}(593,\cdot)\) \(\chi_{2001}(602,\cdot)\) \(\chi_{2001}(614,\cdot)\) \(\chi_{2001}(647,\cdot)\) \(\chi_{2001}(671,\cdot)\) \(\chi_{2001}(680,\cdot)\) \(\chi_{2001}(731,\cdot)\) \(\chi_{2001}(767,\cdot)\) \(\chi_{2001}(788,\cdot)\) \(\chi_{2001}(818,\cdot)\) \(\chi_{2001}(821,\cdot)\) \(\chi_{2001}(854,\cdot)\) \(\chi_{2001}(863,\cdot)\) \(\chi_{2001}(905,\cdot)\) \(\chi_{2001}(932,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((-1,e\left(\frac{10}{11}\right),e\left(\frac{3}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{101}{154}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{29}{77}\right)\) | \(e\left(\frac{10}{77}\right)\) |