Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(660\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.dp
\(\chi_{4025}(17,\cdot)\) \(\chi_{4025}(33,\cdot)\) \(\chi_{4025}(38,\cdot)\) \(\chi_{4025}(103,\cdot)\) \(\chi_{4025}(122,\cdot)\) \(\chi_{4025}(152,\cdot)\) \(\chi_{4025}(178,\cdot)\) \(\chi_{4025}(222,\cdot)\) \(\chi_{4025}(227,\cdot)\) \(\chi_{4025}(283,\cdot)\) \(\chi_{4025}(297,\cdot)\) \(\chi_{4025}(313,\cdot)\) \(\chi_{4025}(327,\cdot)\) \(\chi_{4025}(362,\cdot)\) \(\chi_{4025}(383,\cdot)\) \(\chi_{4025}(388,\cdot)\) \(\chi_{4025}(402,\cdot)\) \(\chi_{4025}(458,\cdot)\) \(\chi_{4025}(467,\cdot)\) \(\chi_{4025}(488,\cdot)\) \(\chi_{4025}(502,\cdot)\) \(\chi_{4025}(523,\cdot)\) \(\chi_{4025}(563,\cdot)\) \(\chi_{4025}(572,\cdot)\) \(\chi_{4025}(612,\cdot)\) \(\chi_{4025}(628,\cdot)\) \(\chi_{4025}(642,\cdot)\) \(\chi_{4025}(663,\cdot)\) \(\chi_{4025}(677,\cdot)\) \(\chi_{4025}(733,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{660})$ |
Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{5}{6}\right),e\left(\frac{9}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{551}{660}\right)\) | \(e\left(\frac{547}{660}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{111}{220}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{329}{660}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{56}{165}\right)\) |