Basic properties
Modulus: | \(7605\) | |
Conductor: | \(1521\) | 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 \(\chi_{1521}(166,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.fh
\(\chi_{7605}(166,\cdot)\) \(\chi_{7605}(511,\cdot)\) \(\chi_{7605}(751,\cdot)\) \(\chi_{7605}(1096,\cdot)\) \(\chi_{7605}(1336,\cdot)\) \(\chi_{7605}(1681,\cdot)\) \(\chi_{7605}(1921,\cdot)\) \(\chi_{7605}(2266,\cdot)\) \(\chi_{7605}(2506,\cdot)\) \(\chi_{7605}(3091,\cdot)\) \(\chi_{7605}(3436,\cdot)\) \(\chi_{7605}(3676,\cdot)\) \(\chi_{7605}(4021,\cdot)\) \(\chi_{7605}(4261,\cdot)\) \(\chi_{7605}(4606,\cdot)\) \(\chi_{7605}(4846,\cdot)\) \(\chi_{7605}(5191,\cdot)\) \(\chi_{7605}(5776,\cdot)\) \(\chi_{7605}(6016,\cdot)\) \(\chi_{7605}(6361,\cdot)\) \(\chi_{7605}(6601,\cdot)\) \(\chi_{7605}(6946,\cdot)\) \(\chi_{7605}(7186,\cdot)\) \(\chi_{7605}(7531,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{23}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(166, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |