Basic properties
Modulus: | \(7098\) | |
Conductor: | \(169\) | 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 \(\chi_{169}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dx
\(\chi_{7098}(43,\cdot)\) \(\chi_{7098}(127,\cdot)\) \(\chi_{7098}(589,\cdot)\) \(\chi_{7098}(673,\cdot)\) \(\chi_{7098}(1135,\cdot)\) \(\chi_{7098}(1219,\cdot)\) \(\chi_{7098}(1681,\cdot)\) \(\chi_{7098}(1765,\cdot)\) \(\chi_{7098}(2227,\cdot)\) \(\chi_{7098}(2311,\cdot)\) \(\chi_{7098}(2773,\cdot)\) \(\chi_{7098}(2857,\cdot)\) \(\chi_{7098}(3319,\cdot)\) \(\chi_{7098}(3949,\cdot)\) \(\chi_{7098}(4411,\cdot)\) \(\chi_{7098}(4495,\cdot)\) \(\chi_{7098}(4957,\cdot)\) \(\chi_{7098}(5041,\cdot)\) \(\chi_{7098}(5503,\cdot)\) \(\chi_{7098}(5587,\cdot)\) \(\chi_{7098}(6049,\cdot)\) \(\chi_{7098}(6133,\cdot)\) \(\chi_{7098}(6595,\cdot)\) \(\chi_{7098}(6679,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,1,e\left(\frac{5}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(5587, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) |