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 \(\chi_{1183}(289,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.cs
\(\chi_{7098}(289,\cdot)\) \(\chi_{7098}(835,\cdot)\) \(\chi_{7098}(1075,\cdot)\) \(\chi_{7098}(1381,\cdot)\) \(\chi_{7098}(1621,\cdot)\) \(\chi_{7098}(1927,\cdot)\) \(\chi_{7098}(2167,\cdot)\) \(\chi_{7098}(2473,\cdot)\) \(\chi_{7098}(2713,\cdot)\) \(\chi_{7098}(3259,\cdot)\) \(\chi_{7098}(3565,\cdot)\) \(\chi_{7098}(3805,\cdot)\) \(\chi_{7098}(4111,\cdot)\) \(\chi_{7098}(4351,\cdot)\) \(\chi_{7098}(4657,\cdot)\) \(\chi_{7098}(4897,\cdot)\) \(\chi_{7098}(5203,\cdot)\) \(\chi_{7098}(5443,\cdot)\) \(\chi_{7098}(5749,\cdot)\) \(\chi_{7098}(5989,\cdot)\) \(\chi_{7098}(6295,\cdot)\) \(\chi_{7098}(6535,\cdot)\) \(\chi_{7098}(6841,\cdot)\) \(\chi_{7098}(7081,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2 |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{34}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) |