Basic properties
Modulus: | \(2001\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(77\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{667}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bk
\(\chi_{2001}(16,\cdot)\) \(\chi_{2001}(25,\cdot)\) \(\chi_{2001}(49,\cdot)\) \(\chi_{2001}(52,\cdot)\) \(\chi_{2001}(82,\cdot)\) \(\chi_{2001}(94,\cdot)\) \(\chi_{2001}(169,\cdot)\) \(\chi_{2001}(190,\cdot)\) \(\chi_{2001}(223,\cdot)\) \(\chi_{2001}(256,\cdot)\) \(\chi_{2001}(397,\cdot)\) \(\chi_{2001}(400,\cdot)\) \(\chi_{2001}(430,\cdot)\) \(\chi_{2001}(487,\cdot)\) \(\chi_{2001}(538,\cdot)\) \(\chi_{2001}(547,\cdot)\) \(\chi_{2001}(604,\cdot)\) \(\chi_{2001}(616,\cdot)\) \(\chi_{2001}(625,\cdot)\) \(\chi_{2001}(634,\cdot)\) \(\chi_{2001}(703,\cdot)\) \(\chi_{2001}(721,\cdot)\) \(\chi_{2001}(745,\cdot)\) \(\chi_{2001}(748,\cdot)\) \(\chi_{2001}(790,\cdot)\) \(\chi_{2001}(808,\cdot)\) \(\chi_{2001}(832,\cdot)\) \(\chi_{2001}(877,\cdot)\) \(\chi_{2001}(886,\cdot)\) \(\chi_{2001}(922,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((668,1132,553)\) → \((1,e\left(\frac{3}{11}\right),e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{43}{77}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{25}{77}\right)\) |