Basic properties
Modulus: | \(7098\) | |
Conductor: | \(3549\) | 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 \(\chi_{3549}(1109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dh
\(\chi_{7098}(17,\cdot)\) \(\chi_{7098}(257,\cdot)\) \(\chi_{7098}(563,\cdot)\) \(\chi_{7098}(803,\cdot)\) \(\chi_{7098}(1109,\cdot)\) \(\chi_{7098}(1349,\cdot)\) \(\chi_{7098}(1655,\cdot)\) \(\chi_{7098}(1895,\cdot)\) \(\chi_{7098}(2201,\cdot)\) \(\chi_{7098}(2441,\cdot)\) \(\chi_{7098}(2747,\cdot)\) \(\chi_{7098}(2987,\cdot)\) \(\chi_{7098}(3293,\cdot)\) \(\chi_{7098}(3533,\cdot)\) \(\chi_{7098}(3839,\cdot)\) \(\chi_{7098}(4385,\cdot)\) \(\chi_{7098}(4625,\cdot)\) \(\chi_{7098}(4931,\cdot)\) \(\chi_{7098}(5171,\cdot)\) \(\chi_{7098}(5477,\cdot)\) \(\chi_{7098}(5717,\cdot)\) \(\chi_{7098}(6023,\cdot)\) \(\chi_{7098}(6263,\cdot)\) \(\chi_{7098}(6809,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{37}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(1109, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{25}{78}\right)\) |