Basic properties
| Modulus: | \(3450\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3450.bl
\(\chi_{3450}(19,\cdot)\) \(\chi_{3450}(79,\cdot)\) \(\chi_{3450}(109,\cdot)\) \(\chi_{3450}(319,\cdot)\) \(\chi_{3450}(379,\cdot)\) \(\chi_{3450}(559,\cdot)\) \(\chi_{3450}(589,\cdot)\) \(\chi_{3450}(619,\cdot)\) \(\chi_{3450}(709,\cdot)\) \(\chi_{3450}(769,\cdot)\) \(\chi_{3450}(889,\cdot)\) \(\chi_{3450}(1009,\cdot)\) \(\chi_{3450}(1069,\cdot)\) \(\chi_{3450}(1279,\cdot)\) \(\chi_{3450}(1309,\cdot)\) \(\chi_{3450}(1339,\cdot)\) \(\chi_{3450}(1459,\cdot)\) \(\chi_{3450}(1489,\cdot)\) \(\chi_{3450}(1579,\cdot)\) \(\chi_{3450}(1759,\cdot)\) \(\chi_{3450}(1939,\cdot)\) \(\chi_{3450}(1969,\cdot)\) \(\chi_{3450}(2029,\cdot)\) \(\chi_{3450}(2089,\cdot)\) \(\chi_{3450}(2179,\cdot)\) \(\chi_{3450}(2269,\cdot)\) \(\chi_{3450}(2389,\cdot)\) \(\chi_{3450}(2629,\cdot)\) \(\chi_{3450}(2659,\cdot)\) \(\chi_{3450}(2689,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3450 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) |