Basic properties
| Modulus: | \(7098\) | |
| Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3549}(3173,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.de
\(\chi_{7098}(53,\cdot)\) \(\chi_{7098}(443,\cdot)\) \(\chi_{7098}(599,\cdot)\) \(\chi_{7098}(989,\cdot)\) \(\chi_{7098}(1145,\cdot)\) \(\chi_{7098}(1535,\cdot)\) \(\chi_{7098}(2081,\cdot)\) \(\chi_{7098}(2237,\cdot)\) \(\chi_{7098}(2627,\cdot)\) \(\chi_{7098}(2783,\cdot)\) \(\chi_{7098}(3173,\cdot)\) \(\chi_{7098}(3329,\cdot)\) \(\chi_{7098}(3875,\cdot)\) \(\chi_{7098}(4265,\cdot)\) \(\chi_{7098}(4421,\cdot)\) \(\chi_{7098}(4811,\cdot)\) \(\chi_{7098}(4967,\cdot)\) \(\chi_{7098}(5357,\cdot)\) \(\chi_{7098}(5513,\cdot)\) \(\chi_{7098}(5903,\cdot)\) \(\chi_{7098}(6059,\cdot)\) \(\chi_{7098}(6449,\cdot)\) \(\chi_{7098}(6605,\cdot)\) \(\chi_{7098}(6995,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{12}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(3173, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) |