Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(4056\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4056}(2309,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.ed
\(\chi_{8112}(281,\cdot)\) \(\chi_{8112}(473,\cdot)\) \(\chi_{8112}(905,\cdot)\) \(\chi_{8112}(1097,\cdot)\) \(\chi_{8112}(1529,\cdot)\) \(\chi_{8112}(1721,\cdot)\) \(\chi_{8112}(2153,\cdot)\) \(\chi_{8112}(2345,\cdot)\) \(\chi_{8112}(2777,\cdot)\) \(\chi_{8112}(2969,\cdot)\) \(\chi_{8112}(3401,\cdot)\) \(\chi_{8112}(3593,\cdot)\) \(\chi_{8112}(4025,\cdot)\) \(\chi_{8112}(4217,\cdot)\) \(\chi_{8112}(4649,\cdot)\) \(\chi_{8112}(4841,\cdot)\) \(\chi_{8112}(5273,\cdot)\) \(\chi_{8112}(5465,\cdot)\) \(\chi_{8112}(5897,\cdot)\) \(\chi_{8112}(6089,\cdot)\) \(\chi_{8112}(6713,\cdot)\) \(\chi_{8112}(7145,\cdot)\) \(\chi_{8112}(7769,\cdot)\) \(\chi_{8112}(7961,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((1,-1,-1,e\left(\frac{37}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(281, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) |