Basic properties
Modulus: | \(3450\) | |
Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{575}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3450.bk
\(\chi_{3450}(31,\cdot)\) \(\chi_{3450}(121,\cdot)\) \(\chi_{3450}(211,\cdot)\) \(\chi_{3450}(271,\cdot)\) \(\chi_{3450}(331,\cdot)\) \(\chi_{3450}(361,\cdot)\) \(\chi_{3450}(541,\cdot)\) \(\chi_{3450}(721,\cdot)\) \(\chi_{3450}(811,\cdot)\) \(\chi_{3450}(841,\cdot)\) \(\chi_{3450}(961,\cdot)\) \(\chi_{3450}(991,\cdot)\) \(\chi_{3450}(1021,\cdot)\) \(\chi_{3450}(1231,\cdot)\) \(\chi_{3450}(1291,\cdot)\) \(\chi_{3450}(1411,\cdot)\) \(\chi_{3450}(1531,\cdot)\) \(\chi_{3450}(1591,\cdot)\) \(\chi_{3450}(1681,\cdot)\) \(\chi_{3450}(1711,\cdot)\) \(\chi_{3450}(1741,\cdot)\) \(\chi_{3450}(1921,\cdot)\) \(\chi_{3450}(1981,\cdot)\) \(\chi_{3450}(2191,\cdot)\) \(\chi_{3450}(2221,\cdot)\) \(\chi_{3450}(2281,\cdot)\) \(\chi_{3450}(2341,\cdot)\) \(\chi_{3450}(2371,\cdot)\) \(\chi_{3450}(2431,\cdot)\) \(\chi_{3450}(2611,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{3}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3450 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{4}{11}\right)\) |