Basic properties
Modulus: | \(726\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 726.m
\(\chi_{726}(25,\cdot)\) \(\chi_{726}(31,\cdot)\) \(\chi_{726}(37,\cdot)\) \(\chi_{726}(49,\cdot)\) \(\chi_{726}(91,\cdot)\) \(\chi_{726}(97,\cdot)\) \(\chi_{726}(103,\cdot)\) \(\chi_{726}(115,\cdot)\) \(\chi_{726}(157,\cdot)\) \(\chi_{726}(163,\cdot)\) \(\chi_{726}(169,\cdot)\) \(\chi_{726}(181,\cdot)\) \(\chi_{726}(223,\cdot)\) \(\chi_{726}(229,\cdot)\) \(\chi_{726}(235,\cdot)\) \(\chi_{726}(247,\cdot)\) \(\chi_{726}(289,\cdot)\) \(\chi_{726}(295,\cdot)\) \(\chi_{726}(301,\cdot)\) \(\chi_{726}(313,\cdot)\) \(\chi_{726}(355,\cdot)\) \(\chi_{726}(361,\cdot)\) \(\chi_{726}(367,\cdot)\) \(\chi_{726}(379,\cdot)\) \(\chi_{726}(421,\cdot)\) \(\chi_{726}(427,\cdot)\) \(\chi_{726}(433,\cdot)\) \(\chi_{726}(445,\cdot)\) \(\chi_{726}(499,\cdot)\) \(\chi_{726}(553,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((485,607)\) → \((1,e\left(\frac{43}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 726 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) |