Basic properties
Modulus: | \(7605\) | |
Conductor: | \(169\) | 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 \(\chi_{169}(68,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.eg
\(\chi_{7605}(406,\cdot)\) \(\chi_{7605}(451,\cdot)\) \(\chi_{7605}(1576,\cdot)\) \(\chi_{7605}(1621,\cdot)\) \(\chi_{7605}(2161,\cdot)\) \(\chi_{7605}(2206,\cdot)\) \(\chi_{7605}(2746,\cdot)\) \(\chi_{7605}(2791,\cdot)\) \(\chi_{7605}(3331,\cdot)\) \(\chi_{7605}(3376,\cdot)\) \(\chi_{7605}(3916,\cdot)\) \(\chi_{7605}(3961,\cdot)\) \(\chi_{7605}(4501,\cdot)\) \(\chi_{7605}(4546,\cdot)\) \(\chi_{7605}(5086,\cdot)\) \(\chi_{7605}(5131,\cdot)\) \(\chi_{7605}(5671,\cdot)\) \(\chi_{7605}(5716,\cdot)\) \(\chi_{7605}(6256,\cdot)\) \(\chi_{7605}(6301,\cdot)\) \(\chi_{7605}(6841,\cdot)\) \(\chi_{7605}(6886,\cdot)\) \(\chi_{7605}(7426,\cdot)\) \(\chi_{7605}(7471,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((6761,1522,6931)\) → \((1,1,e\left(\frac{37}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(406, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |