Basic properties
Modulus: | \(7056\) | |
Conductor: | \(2352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2352}(269,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7056.iz
\(\chi_{7056}(269,\cdot)\) \(\chi_{7056}(341,\cdot)\) \(\chi_{7056}(773,\cdot)\) \(\chi_{7056}(845,\cdot)\) \(\chi_{7056}(1277,\cdot)\) \(\chi_{7056}(1349,\cdot)\) \(\chi_{7056}(1781,\cdot)\) \(\chi_{7056}(1853,\cdot)\) \(\chi_{7056}(2357,\cdot)\) \(\chi_{7056}(2789,\cdot)\) \(\chi_{7056}(3293,\cdot)\) \(\chi_{7056}(3365,\cdot)\) \(\chi_{7056}(3797,\cdot)\) \(\chi_{7056}(3869,\cdot)\) \(\chi_{7056}(4301,\cdot)\) \(\chi_{7056}(4373,\cdot)\) \(\chi_{7056}(4805,\cdot)\) \(\chi_{7056}(4877,\cdot)\) \(\chi_{7056}(5309,\cdot)\) \(\chi_{7056}(5381,\cdot)\) \(\chi_{7056}(5885,\cdot)\) \(\chi_{7056}(6317,\cdot)\) \(\chi_{7056}(6821,\cdot)\) \(\chi_{7056}(6893,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,-i,-1,e\left(\frac{37}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(269, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{79}{84}\right)\) |