Basic properties
Modulus: | \(5929\) | |
Conductor: | \(5929\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(77\) | 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 5929.bl
\(\chi_{5929}(78,\cdot)\) \(\chi_{5929}(155,\cdot)\) \(\chi_{5929}(232,\cdot)\) \(\chi_{5929}(309,\cdot)\) \(\chi_{5929}(386,\cdot)\) \(\chi_{5929}(463,\cdot)\) \(\chi_{5929}(617,\cdot)\) \(\chi_{5929}(694,\cdot)\) \(\chi_{5929}(771,\cdot)\) \(\chi_{5929}(925,\cdot)\) \(\chi_{5929}(1002,\cdot)\) \(\chi_{5929}(1156,\cdot)\) \(\chi_{5929}(1233,\cdot)\) \(\chi_{5929}(1310,\cdot)\) \(\chi_{5929}(1387,\cdot)\) \(\chi_{5929}(1464,\cdot)\) \(\chi_{5929}(1541,\cdot)\) \(\chi_{5929}(1772,\cdot)\) \(\chi_{5929}(1849,\cdot)\) \(\chi_{5929}(1926,\cdot)\) \(\chi_{5929}(2003,\cdot)\) \(\chi_{5929}(2080,\cdot)\) \(\chi_{5929}(2234,\cdot)\) \(\chi_{5929}(2311,\cdot)\) \(\chi_{5929}(2388,\cdot)\) \(\chi_{5929}(2465,\cdot)\) \(\chi_{5929}(2619,\cdot)\) \(\chi_{5929}(2773,\cdot)\) \(\chi_{5929}(2850,\cdot)\) \(\chi_{5929}(2927,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((1816,2059)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{8}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
\( \chi_{ 5929 }(78, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{46}{77}\right)\) |