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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bn
\(\chi_{2001}(20,\cdot)\) \(\chi_{2001}(53,\cdot)\) \(\chi_{2001}(65,\cdot)\) \(\chi_{2001}(74,\cdot)\) \(\chi_{2001}(83,\cdot)\) \(\chi_{2001}(107,\cdot)\) \(\chi_{2001}(152,\cdot)\) \(\chi_{2001}(194,\cdot)\) \(\chi_{2001}(227,\cdot)\) \(\chi_{2001}(281,\cdot)\) \(\chi_{2001}(314,\cdot)\) \(\chi_{2001}(401,\cdot)\) \(\chi_{2001}(431,\cdot)\) \(\chi_{2001}(458,\cdot)\) \(\chi_{2001}(488,\cdot)\) \(\chi_{2001}(500,\cdot)\) \(\chi_{2001}(596,\cdot)\) \(\chi_{2001}(605,\cdot)\) \(\chi_{2001}(632,\cdot)\) \(\chi_{2001}(674,\cdot)\) \(\chi_{2001}(770,\cdot)\) \(\chi_{2001}(779,\cdot)\) \(\chi_{2001}(803,\cdot)\) \(\chi_{2001}(848,\cdot)\) \(\chi_{2001}(866,\cdot)\) \(\chi_{2001}(893,\cdot)\) \(\chi_{2001}(935,\cdot)\) \(\chi_{2001}(953,\cdot)\) \(\chi_{2001}(977,\cdot)\) \(\chi_{2001}(980,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((-1,e\left(\frac{13}{22}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(596, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{154}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{18}{77}\right)\) | \(e\left(\frac{145}{154}\right)\) | \(e\left(\frac{73}{154}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{23}{77}\right)\) |