Basic properties
| Modulus: | \(5550\) | |
| Conductor: | \(2775\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2775}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5550.ei
\(\chi_{5550}(53,\cdot)\) \(\chi_{5550}(83,\cdot)\) \(\chi_{5550}(197,\cdot)\) \(\chi_{5550}(377,\cdot)\) \(\chi_{5550}(497,\cdot)\) \(\chi_{5550}(527,\cdot)\) \(\chi_{5550}(737,\cdot)\) \(\chi_{5550}(773,\cdot)\) \(\chi_{5550}(863,\cdot)\) \(\chi_{5550}(1163,\cdot)\) \(\chi_{5550}(1217,\cdot)\) \(\chi_{5550}(1403,\cdot)\) \(\chi_{5550}(1487,\cdot)\) \(\chi_{5550}(1637,\cdot)\) \(\chi_{5550}(1847,\cdot)\) \(\chi_{5550}(1883,\cdot)\) \(\chi_{5550}(1973,\cdot)\) \(\chi_{5550}(2153,\cdot)\) \(\chi_{5550}(2273,\cdot)\) \(\chi_{5550}(2303,\cdot)\) \(\chi_{5550}(2327,\cdot)\) \(\chi_{5550}(2417,\cdot)\) \(\chi_{5550}(2513,\cdot)\) \(\chi_{5550}(2597,\cdot)\) \(\chi_{5550}(2717,\cdot)\) \(\chi_{5550}(2747,\cdot)\) \(\chi_{5550}(3083,\cdot)\) \(\chi_{5550}(3263,\cdot)\) \(\chi_{5550}(3383,\cdot)\) \(\chi_{5550}(3413,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((3701,1777,2851)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(41\) | \(43\) |
| \( \chi_{ 5550 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(i\) |