Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(74,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.cq
\(\chi_{7098}(211,\cdot)\) \(\chi_{7098}(295,\cdot)\) \(\chi_{7098}(757,\cdot)\) \(\chi_{7098}(841,\cdot)\) \(\chi_{7098}(1303,\cdot)\) \(\chi_{7098}(1387,\cdot)\) \(\chi_{7098}(1849,\cdot)\) \(\chi_{7098}(1933,\cdot)\) \(\chi_{7098}(2395,\cdot)\) \(\chi_{7098}(2479,\cdot)\) \(\chi_{7098}(2941,\cdot)\) \(\chi_{7098}(3025,\cdot)\) \(\chi_{7098}(3487,\cdot)\) \(\chi_{7098}(4117,\cdot)\) \(\chi_{7098}(4579,\cdot)\) \(\chi_{7098}(4663,\cdot)\) \(\chi_{7098}(5125,\cdot)\) \(\chi_{7098}(5209,\cdot)\) \(\chi_{7098}(5671,\cdot)\) \(\chi_{7098}(5755,\cdot)\) \(\chi_{7098}(6217,\cdot)\) \(\chi_{7098}(6301,\cdot)\) \(\chi_{7098}(6763,\cdot)\) \(\chi_{7098}(6847,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,1,e\left(\frac{38}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(1933, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) |