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 \(\chi_{667}(303,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bo
\(\chi_{2001}(4,\cdot)\) \(\chi_{2001}(13,\cdot)\) \(\chi_{2001}(64,\cdot)\) \(\chi_{2001}(100,\cdot)\) \(\chi_{2001}(121,\cdot)\) \(\chi_{2001}(151,\cdot)\) \(\chi_{2001}(154,\cdot)\) \(\chi_{2001}(187,\cdot)\) \(\chi_{2001}(196,\cdot)\) \(\chi_{2001}(238,\cdot)\) \(\chi_{2001}(265,\cdot)\) \(\chi_{2001}(325,\cdot)\) \(\chi_{2001}(328,\cdot)\) \(\chi_{2001}(361,\cdot)\) \(\chi_{2001}(370,\cdot)\) \(\chi_{2001}(439,\cdot)\) \(\chi_{2001}(469,\cdot)\) \(\chi_{2001}(499,\cdot)\) \(\chi_{2001}(535,\cdot)\) \(\chi_{2001}(556,\cdot)\) \(\chi_{2001}(673,\cdot)\) \(\chi_{2001}(676,\cdot)\) \(\chi_{2001}(763,\cdot)\) \(\chi_{2001}(817,\cdot)\) \(\chi_{2001}(883,\cdot)\) \(\chi_{2001}(892,\cdot)\) \(\chi_{2001}(961,\cdot)\) \(\chi_{2001}(970,\cdot)\) \(\chi_{2001}(979,\cdot)\) \(\chi_{2001}(991,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((1,e\left(\frac{2}{11}\right),e\left(\frac{9}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(970, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{25}{77}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{109}{154}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{2}{77}\right)\) |