Basic properties
Modulus: | \(5070\) | |
Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{845}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5070.cl
\(\chi_{5070}(139,\cdot)\) \(\chi_{5070}(289,\cdot)\) \(\chi_{5070}(679,\cdot)\) \(\chi_{5070}(919,\cdot)\) \(\chi_{5070}(1069,\cdot)\) \(\chi_{5070}(1309,\cdot)\) \(\chi_{5070}(1459,\cdot)\) \(\chi_{5070}(1699,\cdot)\) \(\chi_{5070}(1849,\cdot)\) \(\chi_{5070}(2089,\cdot)\) \(\chi_{5070}(2239,\cdot)\) \(\chi_{5070}(2479,\cdot)\) \(\chi_{5070}(2629,\cdot)\) \(\chi_{5070}(2869,\cdot)\) \(\chi_{5070}(3259,\cdot)\) \(\chi_{5070}(3409,\cdot)\) \(\chi_{5070}(3649,\cdot)\) \(\chi_{5070}(3799,\cdot)\) \(\chi_{5070}(4039,\cdot)\) \(\chi_{5070}(4189,\cdot)\) \(\chi_{5070}(4429,\cdot)\) \(\chi_{5070}(4579,\cdot)\) \(\chi_{5070}(4819,\cdot)\) \(\chi_{5070}(4969,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1691,4057,1861)\) → \((1,-1,e\left(\frac{14}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 5070 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) |