Basic properties
| Modulus: | \(418\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 418.u
\(\chi_{418}(5,\cdot)\) \(\chi_{418}(9,\cdot)\) \(\chi_{418}(25,\cdot)\) \(\chi_{418}(47,\cdot)\) \(\chi_{418}(81,\cdot)\) \(\chi_{418}(93,\cdot)\) \(\chi_{418}(119,\cdot)\) \(\chi_{418}(137,\cdot)\) \(\chi_{418}(157,\cdot)\) \(\chi_{418}(169,\cdot)\) \(\chi_{418}(207,\cdot)\) \(\chi_{418}(213,\cdot)\) \(\chi_{418}(225,\cdot)\) \(\chi_{418}(245,\cdot)\) \(\chi_{418}(251,\cdot)\) \(\chi_{418}(289,\cdot)\) \(\chi_{418}(291,\cdot)\) \(\chi_{418}(301,\cdot)\) \(\chi_{418}(313,\cdot)\) \(\chi_{418}(339,\cdot)\) \(\chi_{418}(367,\cdot)\) \(\chi_{418}(377,\cdot)\) \(\chi_{418}(389,\cdot)\) \(\chi_{418}(405,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | 45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1 |
Values on generators
\((343,287)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 418 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{29}{45}\right)\) |