Basic properties
Modulus: | \(7098\) | |
Conductor: | \(3549\) | 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 \(\chi_{3549}(797,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dz
\(\chi_{7098}(251,\cdot)\) \(\chi_{7098}(335,\cdot)\) \(\chi_{7098}(797,\cdot)\) \(\chi_{7098}(881,\cdot)\) \(\chi_{7098}(1343,\cdot)\) \(\chi_{7098}(1427,\cdot)\) \(\chi_{7098}(1889,\cdot)\) \(\chi_{7098}(1973,\cdot)\) \(\chi_{7098}(2435,\cdot)\) \(\chi_{7098}(2519,\cdot)\) \(\chi_{7098}(2981,\cdot)\) \(\chi_{7098}(3611,\cdot)\) \(\chi_{7098}(4073,\cdot)\) \(\chi_{7098}(4157,\cdot)\) \(\chi_{7098}(4619,\cdot)\) \(\chi_{7098}(4703,\cdot)\) \(\chi_{7098}(5165,\cdot)\) \(\chi_{7098}(5249,\cdot)\) \(\chi_{7098}(5711,\cdot)\) \(\chi_{7098}(5795,\cdot)\) \(\chi_{7098}(6257,\cdot)\) \(\chi_{7098}(6341,\cdot)\) \(\chi_{7098}(6803,\cdot)\) \(\chi_{7098}(6887,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,-1,e\left(\frac{25}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(797, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{19}{78}\right)\) |