Basic properties
| Modulus: | \(3450\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3450.bu
\(\chi_{3450}(13,\cdot)\) \(\chi_{3450}(73,\cdot)\) \(\chi_{3450}(127,\cdot)\) \(\chi_{3450}(133,\cdot)\) \(\chi_{3450}(163,\cdot)\) \(\chi_{3450}(187,\cdot)\) \(\chi_{3450}(223,\cdot)\) \(\chi_{3450}(397,\cdot)\) \(\chi_{3450}(403,\cdot)\) \(\chi_{3450}(427,\cdot)\) \(\chi_{3450}(463,\cdot)\) \(\chi_{3450}(487,\cdot)\) \(\chi_{3450}(547,\cdot)\) \(\chi_{3450}(577,\cdot)\) \(\chi_{3450}(583,\cdot)\) \(\chi_{3450}(637,\cdot)\) \(\chi_{3450}(673,\cdot)\) \(\chi_{3450}(703,\cdot)\) \(\chi_{3450}(763,\cdot)\) \(\chi_{3450}(817,\cdot)\) \(\chi_{3450}(823,\cdot)\) \(\chi_{3450}(853,\cdot)\) \(\chi_{3450}(877,\cdot)\) \(\chi_{3450}(883,\cdot)\) \(\chi_{3450}(913,\cdot)\) \(\chi_{3450}(997,\cdot)\) \(\chi_{3450}(1087,\cdot)\) \(\chi_{3450}(1117,\cdot)\) \(\chi_{3450}(1153,\cdot)\) \(\chi_{3450}(1177,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{11}{20}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3450 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{93}{220}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{7}{44}\right)\) |