Basic properties
Modulus: | \(7098\) | |
Conductor: | \(1183\) | 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 \(\chi_{1183}(205,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dd
\(\chi_{7098}(205,\cdot)\) \(\chi_{7098}(277,\cdot)\) \(\chi_{7098}(751,\cdot)\) \(\chi_{7098}(1297,\cdot)\) \(\chi_{7098}(1369,\cdot)\) \(\chi_{7098}(1843,\cdot)\) \(\chi_{7098}(1915,\cdot)\) \(\chi_{7098}(2461,\cdot)\) \(\chi_{7098}(2935,\cdot)\) \(\chi_{7098}(3007,\cdot)\) \(\chi_{7098}(3481,\cdot)\) \(\chi_{7098}(3553,\cdot)\) \(\chi_{7098}(4027,\cdot)\) \(\chi_{7098}(4099,\cdot)\) \(\chi_{7098}(4573,\cdot)\) \(\chi_{7098}(4645,\cdot)\) \(\chi_{7098}(5119,\cdot)\) \(\chi_{7098}(5191,\cdot)\) \(\chi_{7098}(5665,\cdot)\) \(\chi_{7098}(5737,\cdot)\) \(\chi_{7098}(6211,\cdot)\) \(\chi_{7098}(6283,\cdot)\) \(\chi_{7098}(6757,\cdot)\) \(\chi_{7098}(6829,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{47}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(205, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{17}{78}\right)\) |