Basic properties
| Modulus: | \(4005\) | |
| Conductor: | \(267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{267}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.dm
\(\chi_{4005}(26,\cdot)\) \(\chi_{4005}(116,\cdot)\) \(\chi_{4005}(206,\cdot)\) \(\chi_{4005}(296,\cdot)\) \(\chi_{4005}(341,\cdot)\) \(\chi_{4005}(386,\cdot)\) \(\chi_{4005}(431,\cdot)\) \(\chi_{4005}(476,\cdot)\) \(\chi_{4005}(521,\cdot)\) \(\chi_{4005}(656,\cdot)\) \(\chi_{4005}(836,\cdot)\) \(\chi_{4005}(1061,\cdot)\) \(\chi_{4005}(1106,\cdot)\) \(\chi_{4005}(1151,\cdot)\) \(\chi_{4005}(1376,\cdot)\) \(\chi_{4005}(1421,\cdot)\) \(\chi_{4005}(1556,\cdot)\) \(\chi_{4005}(1826,\cdot)\) \(\chi_{4005}(1961,\cdot)\) \(\chi_{4005}(2006,\cdot)\) \(\chi_{4005}(2231,\cdot)\) \(\chi_{4005}(2276,\cdot)\) \(\chi_{4005}(2321,\cdot)\) \(\chi_{4005}(2546,\cdot)\) \(\chi_{4005}(2726,\cdot)\) \(\chi_{4005}(2861,\cdot)\) \(\chi_{4005}(2906,\cdot)\) \(\chi_{4005}(2951,\cdot)\) \(\chi_{4005}(2996,\cdot)\) \(\chi_{4005}(3041,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((3116,802,181)\) → \((-1,1,e\left(\frac{39}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{45}{88}\right)\) |