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 \(\chi_{575}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3450.bt
\(\chi_{3450}(37,\cdot)\) \(\chi_{3450}(67,\cdot)\) \(\chi_{3450}(97,\cdot)\) \(\chi_{3450}(103,\cdot)\) \(\chi_{3450}(217,\cdot)\) \(\chi_{3450}(247,\cdot)\) \(\chi_{3450}(283,\cdot)\) \(\chi_{3450}(313,\cdot)\) \(\chi_{3450}(337,\cdot)\) \(\chi_{3450}(373,\cdot)\) \(\chi_{3450}(433,\cdot)\) \(\chi_{3450}(517,\cdot)\) \(\chi_{3450}(523,\cdot)\) \(\chi_{3450}(613,\cdot)\) \(\chi_{3450}(697,\cdot)\) \(\chi_{3450}(727,\cdot)\) \(\chi_{3450}(733,\cdot)\) \(\chi_{3450}(787,\cdot)\) \(\chi_{3450}(847,\cdot)\) \(\chi_{3450}(937,\cdot)\) \(\chi_{3450}(973,\cdot)\) \(\chi_{3450}(1003,\cdot)\) \(\chi_{3450}(1027,\cdot)\) \(\chi_{3450}(1033,\cdot)\) \(\chi_{3450}(1063,\cdot)\) \(\chi_{3450}(1123,\cdot)\) \(\chi_{3450}(1147,\cdot)\) \(\chi_{3450}(1183,\cdot)\) \(\chi_{3450}(1213,\cdot)\) \(\chi_{3450}(1303,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{9}{20}\right),e\left(\frac{21}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3450 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{117}{220}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{23}{44}\right)\) |