Basic properties
| Modulus: | \(162240\) | |
| Conductor: | \(40560\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{40560}(4763,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 162240.xa
\(\chi_{162240}(47,\cdot)\) \(\chi_{162240}(3983,\cdot)\) \(\chi_{162240}(12527,\cdot)\) \(\chi_{162240}(25007,\cdot)\) \(\chi_{162240}(28943,\cdot)\) \(\chi_{162240}(37487,\cdot)\) \(\chi_{162240}(41423,\cdot)\) \(\chi_{162240}(49967,\cdot)\) \(\chi_{162240}(53903,\cdot)\) \(\chi_{162240}(62447,\cdot)\) \(\chi_{162240}(66383,\cdot)\) \(\chi_{162240}(74927,\cdot)\) \(\chi_{162240}(78863,\cdot)\) \(\chi_{162240}(87407,\cdot)\) \(\chi_{162240}(91343,\cdot)\) \(\chi_{162240}(99887,\cdot)\) \(\chi_{162240}(103823,\cdot)\) \(\chi_{162240}(112367,\cdot)\) \(\chi_{162240}(116303,\cdot)\) \(\chi_{162240}(124847,\cdot)\) \(\chi_{162240}(128783,\cdot)\) \(\chi_{162240}(141263,\cdot)\) \(\chi_{162240}(149807,\cdot)\) \(\chi_{162240}(153743,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((45631,70981,108161,64897,93121)\) → \((-1,i,-1,-i,e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 162240 }(116303, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) |