Basic properties
| Modulus: | \(3450\) | |
| Conductor: | \(1725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1725}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3450.br
\(\chi_{3450}(11,\cdot)\) \(\chi_{3450}(191,\cdot)\) \(\chi_{3450}(221,\cdot)\) \(\chi_{3450}(281,\cdot)\) \(\chi_{3450}(341,\cdot)\) \(\chi_{3450}(431,\cdot)\) \(\chi_{3450}(521,\cdot)\) \(\chi_{3450}(641,\cdot)\) \(\chi_{3450}(881,\cdot)\) \(\chi_{3450}(911,\cdot)\) \(\chi_{3450}(941,\cdot)\) \(\chi_{3450}(971,\cdot)\) \(\chi_{3450}(1031,\cdot)\) \(\chi_{3450}(1091,\cdot)\) \(\chi_{3450}(1121,\cdot)\) \(\chi_{3450}(1211,\cdot)\) \(\chi_{3450}(1331,\cdot)\) \(\chi_{3450}(1391,\cdot)\) \(\chi_{3450}(1571,\cdot)\) \(\chi_{3450}(1631,\cdot)\) \(\chi_{3450}(1661,\cdot)\) \(\chi_{3450}(1721,\cdot)\) \(\chi_{3450}(1781,\cdot)\) \(\chi_{3450}(1811,\cdot)\) \(\chi_{3450}(2021,\cdot)\) \(\chi_{3450}(2081,\cdot)\) \(\chi_{3450}(2261,\cdot)\) \(\chi_{3450}(2291,\cdot)\) \(\chi_{3450}(2321,\cdot)\) \(\chi_{3450}(2411,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3450 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{1}{22}\right)\) |