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 \(\chi_{1183}(1122,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dm
\(\chi_{7098}(121,\cdot)\) \(\chi_{7098}(667,\cdot)\) \(\chi_{7098}(907,\cdot)\) \(\chi_{7098}(1213,\cdot)\) \(\chi_{7098}(1453,\cdot)\) \(\chi_{7098}(1759,\cdot)\) \(\chi_{7098}(1999,\cdot)\) \(\chi_{7098}(2305,\cdot)\) \(\chi_{7098}(2545,\cdot)\) \(\chi_{7098}(3091,\cdot)\) \(\chi_{7098}(3397,\cdot)\) \(\chi_{7098}(3637,\cdot)\) \(\chi_{7098}(3943,\cdot)\) \(\chi_{7098}(4183,\cdot)\) \(\chi_{7098}(4489,\cdot)\) \(\chi_{7098}(4729,\cdot)\) \(\chi_{7098}(5035,\cdot)\) \(\chi_{7098}(5275,\cdot)\) \(\chi_{7098}(5581,\cdot)\) \(\chi_{7098}(5821,\cdot)\) \(\chi_{7098}(6127,\cdot)\) \(\chi_{7098}(6367,\cdot)\) \(\chi_{7098}(6673,\cdot)\) \(\chi_{7098}(6913,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{31}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(2305, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) |