Basic properties
Modulus: | \(7098\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(354,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.cr
\(\chi_{7098}(373,\cdot)\) \(\chi_{7098}(445,\cdot)\) \(\chi_{7098}(919,\cdot)\) \(\chi_{7098}(1465,\cdot)\) \(\chi_{7098}(1537,\cdot)\) \(\chi_{7098}(2011,\cdot)\) \(\chi_{7098}(2083,\cdot)\) \(\chi_{7098}(2629,\cdot)\) \(\chi_{7098}(3103,\cdot)\) \(\chi_{7098}(3175,\cdot)\) \(\chi_{7098}(3649,\cdot)\) \(\chi_{7098}(3721,\cdot)\) \(\chi_{7098}(4195,\cdot)\) \(\chi_{7098}(4267,\cdot)\) \(\chi_{7098}(4741,\cdot)\) \(\chi_{7098}(4813,\cdot)\) \(\chi_{7098}(5287,\cdot)\) \(\chi_{7098}(5359,\cdot)\) \(\chi_{7098}(5833,\cdot)\) \(\chi_{7098}(5905,\cdot)\) \(\chi_{7098}(6379,\cdot)\) \(\chi_{7098}(6451,\cdot)\) \(\chi_{7098}(6925,\cdot)\) \(\chi_{7098}(6997,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1 |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{1}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(1537, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) |