Basic properties
| Modulus: | \(5400\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5400.ei
\(\chi_{5400}(121,\cdot)\) \(\chi_{5400}(241,\cdot)\) \(\chi_{5400}(481,\cdot)\) \(\chi_{5400}(841,\cdot)\) \(\chi_{5400}(961,\cdot)\) \(\chi_{5400}(1321,\cdot)\) \(\chi_{5400}(1561,\cdot)\) \(\chi_{5400}(1681,\cdot)\) \(\chi_{5400}(1921,\cdot)\) \(\chi_{5400}(2041,\cdot)\) \(\chi_{5400}(2281,\cdot)\) \(\chi_{5400}(2641,\cdot)\) \(\chi_{5400}(2761,\cdot)\) \(\chi_{5400}(3121,\cdot)\) \(\chi_{5400}(3361,\cdot)\) \(\chi_{5400}(3481,\cdot)\) \(\chi_{5400}(3721,\cdot)\) \(\chi_{5400}(3841,\cdot)\) \(\chi_{5400}(4081,\cdot)\) \(\chi_{5400}(4441,\cdot)\) \(\chi_{5400}(4561,\cdot)\) \(\chi_{5400}(4921,\cdot)\) \(\chi_{5400}(5161,\cdot)\) \(\chi_{5400}(5281,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1351,2701,1001,2377)\) → \((1,1,e\left(\frac{4}{9}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5400 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{43}{45}\right)\) |