Basic properties
Modulus: | \(418\) | |
Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{209}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 418.v
\(\chi_{418}(13,\cdot)\) \(\chi_{418}(29,\cdot)\) \(\chi_{418}(41,\cdot)\) \(\chi_{418}(51,\cdot)\) \(\chi_{418}(79,\cdot)\) \(\chi_{418}(105,\cdot)\) \(\chi_{418}(117,\cdot)\) \(\chi_{418}(127,\cdot)\) \(\chi_{418}(129,\cdot)\) \(\chi_{418}(167,\cdot)\) \(\chi_{418}(173,\cdot)\) \(\chi_{418}(193,\cdot)\) \(\chi_{418}(205,\cdot)\) \(\chi_{418}(211,\cdot)\) \(\chi_{418}(249,\cdot)\) \(\chi_{418}(261,\cdot)\) \(\chi_{418}(281,\cdot)\) \(\chi_{418}(299,\cdot)\) \(\chi_{418}(325,\cdot)\) \(\chi_{418}(337,\cdot)\) \(\chi_{418}(371,\cdot)\) \(\chi_{418}(393,\cdot)\) \(\chi_{418}(409,\cdot)\) \(\chi_{418}(413,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((343,287)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 418 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{31}{45}\right)\) |