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 \(\chi_{3549}(1595,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.cz
\(\chi_{7098}(419,\cdot)\) \(\chi_{7098}(503,\cdot)\) \(\chi_{7098}(965,\cdot)\) \(\chi_{7098}(1049,\cdot)\) \(\chi_{7098}(1511,\cdot)\) \(\chi_{7098}(1595,\cdot)\) \(\chi_{7098}(2057,\cdot)\) \(\chi_{7098}(2141,\cdot)\) \(\chi_{7098}(2603,\cdot)\) \(\chi_{7098}(2687,\cdot)\) \(\chi_{7098}(3149,\cdot)\) \(\chi_{7098}(3779,\cdot)\) \(\chi_{7098}(4241,\cdot)\) \(\chi_{7098}(4325,\cdot)\) \(\chi_{7098}(4787,\cdot)\) \(\chi_{7098}(4871,\cdot)\) \(\chi_{7098}(5333,\cdot)\) \(\chi_{7098}(5417,\cdot)\) \(\chi_{7098}(5879,\cdot)\) \(\chi_{7098}(5963,\cdot)\) \(\chi_{7098}(6425,\cdot)\) \(\chi_{7098}(6509,\cdot)\) \(\chi_{7098}(6971,\cdot)\) \(\chi_{7098}(7055,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,-1,e\left(\frac{38}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(1595, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) |