Basic properties
| Modulus: | \(5550\) | |
| Conductor: | \(925\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{925}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5550.ee
\(\chi_{5550}(13,\cdot)\) \(\chi_{5550}(133,\cdot)\) \(\chi_{5550}(187,\cdot)\) \(\chi_{5550}(217,\cdot)\) \(\chi_{5550}(277,\cdot)\) \(\chi_{5550}(313,\cdot)\) \(\chi_{5550}(427,\cdot)\) \(\chi_{5550}(463,\cdot)\) \(\chi_{5550}(523,\cdot)\) \(\chi_{5550}(553,\cdot)\) \(\chi_{5550}(727,\cdot)\) \(\chi_{5550}(1123,\cdot)\) \(\chi_{5550}(1297,\cdot)\) \(\chi_{5550}(1327,\cdot)\) \(\chi_{5550}(1387,\cdot)\) \(\chi_{5550}(1423,\cdot)\) \(\chi_{5550}(1537,\cdot)\) \(\chi_{5550}(1573,\cdot)\) \(\chi_{5550}(1633,\cdot)\) \(\chi_{5550}(1663,\cdot)\) \(\chi_{5550}(1717,\cdot)\) \(\chi_{5550}(1837,\cdot)\) \(\chi_{5550}(2233,\cdot)\) \(\chi_{5550}(2353,\cdot)\) \(\chi_{5550}(2437,\cdot)\) \(\chi_{5550}(2497,\cdot)\) \(\chi_{5550}(2533,\cdot)\) \(\chi_{5550}(2647,\cdot)\) \(\chi_{5550}(2683,\cdot)\) \(\chi_{5550}(2773,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((3701,1777,2851)\) → \((1,e\left(\frac{19}{20}\right),e\left(\frac{11}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(41\) | \(43\) |
| \( \chi_{ 5550 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(-1\) |