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.bm
\(\chi_{2001}(110,\cdot)\) \(\chi_{2001}(140,\cdot)\) \(\chi_{2001}(170,\cdot)\) \(\chi_{2001}(197,\cdot)\) \(\chi_{2001}(239,\cdot)\) \(\chi_{2001}(248,\cdot)\) \(\chi_{2001}(257,\cdot)\) \(\chi_{2001}(284,\cdot)\) \(\chi_{2001}(326,\cdot)\) \(\chi_{2001}(335,\cdot)\) \(\chi_{2001}(371,\cdot)\) \(\chi_{2001}(422,\cdot)\) \(\chi_{2001}(455,\cdot)\) \(\chi_{2001}(509,\cdot)\) \(\chi_{2001}(518,\cdot)\) \(\chi_{2001}(542,\cdot)\) \(\chi_{2001}(545,\cdot)\) \(\chi_{2001}(587,\cdot)\) \(\chi_{2001}(629,\cdot)\) \(\chi_{2001}(662,\cdot)\) \(\chi_{2001}(683,\cdot)\) \(\chi_{2001}(692,\cdot)\) \(\chi_{2001}(716,\cdot)\) \(\chi_{2001}(719,\cdot)\) \(\chi_{2001}(749,\cdot)\) \(\chi_{2001}(761,\cdot)\) \(\chi_{2001}(836,\cdot)\) \(\chi_{2001}(857,\cdot)\) \(\chi_{2001}(890,\cdot)\) \(\chi_{2001}(923,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((-1,e\left(\frac{6}{11}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2001 }(110, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{154}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{117}{154}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{141}{154}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{17}{77}\right)\) |