Basic properties
Modulus: | \(810\) | |
Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{405}(178,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 810.x
\(\chi_{810}(7,\cdot)\) \(\chi_{810}(13,\cdot)\) \(\chi_{810}(43,\cdot)\) \(\chi_{810}(67,\cdot)\) \(\chi_{810}(97,\cdot)\) \(\chi_{810}(103,\cdot)\) \(\chi_{810}(133,\cdot)\) \(\chi_{810}(157,\cdot)\) \(\chi_{810}(187,\cdot)\) \(\chi_{810}(193,\cdot)\) \(\chi_{810}(223,\cdot)\) \(\chi_{810}(247,\cdot)\) \(\chi_{810}(277,\cdot)\) \(\chi_{810}(283,\cdot)\) \(\chi_{810}(313,\cdot)\) \(\chi_{810}(337,\cdot)\) \(\chi_{810}(367,\cdot)\) \(\chi_{810}(373,\cdot)\) \(\chi_{810}(403,\cdot)\) \(\chi_{810}(427,\cdot)\) \(\chi_{810}(457,\cdot)\) \(\chi_{810}(463,\cdot)\) \(\chi_{810}(493,\cdot)\) \(\chi_{810}(517,\cdot)\) \(\chi_{810}(547,\cdot)\) \(\chi_{810}(553,\cdot)\) \(\chi_{810}(583,\cdot)\) \(\chi_{810}(607,\cdot)\) \(\chi_{810}(637,\cdot)\) \(\chi_{810}(643,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((731,487)\) → \((e\left(\frac{2}{27}\right),-i)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 810 }(583, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{25}{27}\right)\) |