Basic properties
| Modulus: | \(6378\) | |
| Conductor: | \(1063\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(177\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1063}(997,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6378.q
\(\chi_{6378}(13,\cdot)\) \(\chi_{6378}(25,\cdot)\) \(\chi_{6378}(37,\cdot)\) \(\chi_{6378}(133,\cdot)\) \(\chi_{6378}(169,\cdot)\) \(\chi_{6378}(193,\cdot)\) \(\chi_{6378}(205,\cdot)\) \(\chi_{6378}(295,\cdot)\) \(\chi_{6378}(307,\cdot)\) \(\chi_{6378}(349,\cdot)\) \(\chi_{6378}(481,\cdot)\) \(\chi_{6378}(535,\cdot)\) \(\chi_{6378}(619,\cdot)\) \(\chi_{6378}(625,\cdot)\) \(\chi_{6378}(763,\cdot)\) \(\chi_{6378}(847,\cdot)\) \(\chi_{6378}(907,\cdot)\) \(\chi_{6378}(967,\cdot)\) \(\chi_{6378}(997,\cdot)\) \(\chi_{6378}(1021,\cdot)\) \(\chi_{6378}(1081,\cdot)\) \(\chi_{6378}(1123,\cdot)\) \(\chi_{6378}(1249,\cdot)\) \(\chi_{6378}(1369,\cdot)\) \(\chi_{6378}(1387,\cdot)\) \(\chi_{6378}(1393,\cdot)\) \(\chi_{6378}(1429,\cdot)\) \(\chi_{6378}(1513,\cdot)\) \(\chi_{6378}(1537,\cdot)\) \(\chi_{6378}(1543,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{177})$ |
| Fixed field: | Number field defined by a degree 177 polynomial (not computed) |
Values on generators
\((4253,4255)\) → \((1,e\left(\frac{29}{177}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 6378 }(997, a) \) | \(1\) | \(1\) | \(e\left(\frac{50}{59}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{113}{177}\right)\) | \(e\left(\frac{53}{59}\right)\) | \(e\left(\frac{27}{59}\right)\) | \(e\left(\frac{97}{177}\right)\) | \(e\left(\frac{101}{177}\right)\) | \(e\left(\frac{41}{59}\right)\) | \(e\left(\frac{143}{177}\right)\) | \(e\left(\frac{29}{177}\right)\) |