Basic properties
Modulus: | \(7098\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ct
\(\chi_{7098}(79,\cdot)\) \(\chi_{7098}(235,\cdot)\) \(\chi_{7098}(625,\cdot)\) \(\chi_{7098}(781,\cdot)\) \(\chi_{7098}(1171,\cdot)\) \(\chi_{7098}(1327,\cdot)\) \(\chi_{7098}(1717,\cdot)\) \(\chi_{7098}(1873,\cdot)\) \(\chi_{7098}(2263,\cdot)\) \(\chi_{7098}(2419,\cdot)\) \(\chi_{7098}(2809,\cdot)\) \(\chi_{7098}(2965,\cdot)\) \(\chi_{7098}(3355,\cdot)\) \(\chi_{7098}(3511,\cdot)\) \(\chi_{7098}(3901,\cdot)\) \(\chi_{7098}(4447,\cdot)\) \(\chi_{7098}(4603,\cdot)\) \(\chi_{7098}(4993,\cdot)\) \(\chi_{7098}(5149,\cdot)\) \(\chi_{7098}(5539,\cdot)\) \(\chi_{7098}(5695,\cdot)\) \(\chi_{7098}(6241,\cdot)\) \(\chi_{7098}(6631,\cdot)\) \(\chi_{7098}(6787,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{2}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) |