Basic properties
| Modulus: | \(5400\) | |
| Conductor: | \(5400\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5400.fl
\(\chi_{5400}(77,\cdot)\) \(\chi_{5400}(173,\cdot)\) \(\chi_{5400}(317,\cdot)\) \(\chi_{5400}(437,\cdot)\) \(\chi_{5400}(533,\cdot)\) \(\chi_{5400}(653,\cdot)\) \(\chi_{5400}(677,\cdot)\) \(\chi_{5400}(797,\cdot)\) \(\chi_{5400}(1013,\cdot)\) \(\chi_{5400}(1037,\cdot)\) \(\chi_{5400}(1253,\cdot)\) \(\chi_{5400}(1373,\cdot)\) \(\chi_{5400}(1397,\cdot)\) \(\chi_{5400}(1517,\cdot)\) \(\chi_{5400}(1613,\cdot)\) \(\chi_{5400}(1733,\cdot)\) \(\chi_{5400}(1877,\cdot)\) \(\chi_{5400}(1973,\cdot)\) \(\chi_{5400}(2117,\cdot)\) \(\chi_{5400}(2237,\cdot)\) \(\chi_{5400}(2333,\cdot)\) \(\chi_{5400}(2453,\cdot)\) \(\chi_{5400}(2477,\cdot)\) \(\chi_{5400}(2597,\cdot)\) \(\chi_{5400}(2813,\cdot)\) \(\chi_{5400}(2837,\cdot)\) \(\chi_{5400}(3053,\cdot)\) \(\chi_{5400}(3173,\cdot)\) \(\chi_{5400}(3197,\cdot)\) \(\chi_{5400}(3317,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1351,2701,1001,2377)\) → \((1,-1,e\left(\frac{11}{18}\right),e\left(\frac{1}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5400 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{61}{180}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{49}{180}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{53}{90}\right)\) |