Basic properties
Modulus: | \(7605\) | |
Conductor: | \(7605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.ew
\(\chi_{7605}(4,\cdot)\) \(\chi_{7605}(439,\cdot)\) \(\chi_{7605}(589,\cdot)\) \(\chi_{7605}(1024,\cdot)\) \(\chi_{7605}(1174,\cdot)\) \(\chi_{7605}(1609,\cdot)\) \(\chi_{7605}(1759,\cdot)\) \(\chi_{7605}(2194,\cdot)\) \(\chi_{7605}(2779,\cdot)\) \(\chi_{7605}(2929,\cdot)\) \(\chi_{7605}(3364,\cdot)\) \(\chi_{7605}(3514,\cdot)\) \(\chi_{7605}(3949,\cdot)\) \(\chi_{7605}(4099,\cdot)\) \(\chi_{7605}(4534,\cdot)\) \(\chi_{7605}(4684,\cdot)\) \(\chi_{7605}(5119,\cdot)\) \(\chi_{7605}(5269,\cdot)\) \(\chi_{7605}(5704,\cdot)\) \(\chi_{7605}(5854,\cdot)\) \(\chi_{7605}(6289,\cdot)\) \(\chi_{7605}(6439,\cdot)\) \(\chi_{7605}(6874,\cdot)\) \(\chi_{7605}(7024,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{1}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |