Basic properties
| Modulus: | \(5400\) | |
| Conductor: | \(5400\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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.ev
\(\chi_{5400}(11,\cdot)\) \(\chi_{5400}(131,\cdot)\) \(\chi_{5400}(371,\cdot)\) \(\chi_{5400}(491,\cdot)\) \(\chi_{5400}(731,\cdot)\) \(\chi_{5400}(1091,\cdot)\) \(\chi_{5400}(1211,\cdot)\) \(\chi_{5400}(1571,\cdot)\) \(\chi_{5400}(1811,\cdot)\) \(\chi_{5400}(1931,\cdot)\) \(\chi_{5400}(2171,\cdot)\) \(\chi_{5400}(2291,\cdot)\) \(\chi_{5400}(2531,\cdot)\) \(\chi_{5400}(2891,\cdot)\) \(\chi_{5400}(3011,\cdot)\) \(\chi_{5400}(3371,\cdot)\) \(\chi_{5400}(3611,\cdot)\) \(\chi_{5400}(3731,\cdot)\) \(\chi_{5400}(3971,\cdot)\) \(\chi_{5400}(4091,\cdot)\) \(\chi_{5400}(4331,\cdot)\) \(\chi_{5400}(4691,\cdot)\) \(\chi_{5400}(4811,\cdot)\) \(\chi_{5400}(5171,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1351,2701,1001,2377)\) → \((-1,-1,e\left(\frac{13}{18}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5400 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{43}{90}\right)\) |