Basic properties
Modulus: | \(7098\) | |
Conductor: | \(1183\) | 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 \(\chi_{1183}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dy
\(\chi_{7098}(55,\cdot)\) \(\chi_{7098}(139,\cdot)\) \(\chi_{7098}(601,\cdot)\) \(\chi_{7098}(685,\cdot)\) \(\chi_{7098}(1147,\cdot)\) \(\chi_{7098}(1231,\cdot)\) \(\chi_{7098}(1693,\cdot)\) \(\chi_{7098}(1777,\cdot)\) \(\chi_{7098}(2239,\cdot)\) \(\chi_{7098}(2323,\cdot)\) \(\chi_{7098}(2785,\cdot)\) \(\chi_{7098}(2869,\cdot)\) \(\chi_{7098}(3331,\cdot)\) \(\chi_{7098}(3415,\cdot)\) \(\chi_{7098}(3877,\cdot)\) \(\chi_{7098}(3961,\cdot)\) \(\chi_{7098}(4423,\cdot)\) \(\chi_{7098}(4507,\cdot)\) \(\chi_{7098}(4969,\cdot)\) \(\chi_{7098}(5053,\cdot)\) \(\chi_{7098}(5515,\cdot)\) \(\chi_{7098}(6145,\cdot)\) \(\chi_{7098}(6607,\cdot)\) \(\chi_{7098}(6691,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,-1,e\left(\frac{14}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(139, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) |