Basic properties
| Modulus: | \(8046\) | |
| Conductor: | \(1341\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(222\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1341}(682,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8046.bb
\(\chi_{8046}(235,\cdot)\) \(\chi_{8046}(307,\cdot)\) \(\chi_{8046}(343,\cdot)\) \(\chi_{8046}(451,\cdot)\) \(\chi_{8046}(469,\cdot)\) \(\chi_{8046}(523,\cdot)\) \(\chi_{8046}(559,\cdot)\) \(\chi_{8046}(577,\cdot)\) \(\chi_{8046}(631,\cdot)\) \(\chi_{8046}(739,\cdot)\) \(\chi_{8046}(901,\cdot)\) \(\chi_{8046}(955,\cdot)\) \(\chi_{8046}(1063,\cdot)\) \(\chi_{8046}(1153,\cdot)\) \(\chi_{8046}(1261,\cdot)\) \(\chi_{8046}(1423,\cdot)\) \(\chi_{8046}(1441,\cdot)\) \(\chi_{8046}(1603,\cdot)\) \(\chi_{8046}(1693,\cdot)\) \(\chi_{8046}(1909,\cdot)\) \(\chi_{8046}(1963,\cdot)\) \(\chi_{8046}(2359,\cdot)\) \(\chi_{8046}(2503,\cdot)\) \(\chi_{8046}(2557,\cdot)\) \(\chi_{8046}(2575,\cdot)\) \(\chi_{8046}(2665,\cdot)\) \(\chi_{8046}(2899,\cdot)\) \(\chi_{8046}(2989,\cdot)\) \(\chi_{8046}(3151,\cdot)\) \(\chi_{8046}(3205,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{111})$ |
| Fixed field: | Number field defined by a degree 222 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{47}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8046 }(235, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{111}\right)\) | \(e\left(\frac{95}{111}\right)\) | \(e\left(\frac{199}{222}\right)\) | \(e\left(\frac{221}{222}\right)\) | \(e\left(\frac{28}{37}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{149}{222}\right)\) | \(e\left(\frac{86}{111}\right)\) | \(e\left(\frac{98}{111}\right)\) | \(e\left(\frac{19}{111}\right)\) |