Basic properties
| Modulus: | \(2700\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2700.cm
\(\chi_{2700}(41,\cdot)\) \(\chi_{2700}(221,\cdot)\) \(\chi_{2700}(281,\cdot)\) \(\chi_{2700}(461,\cdot)\) \(\chi_{2700}(581,\cdot)\) \(\chi_{2700}(641,\cdot)\) \(\chi_{2700}(761,\cdot)\) \(\chi_{2700}(821,\cdot)\) \(\chi_{2700}(941,\cdot)\) \(\chi_{2700}(1121,\cdot)\) \(\chi_{2700}(1181,\cdot)\) \(\chi_{2700}(1361,\cdot)\) \(\chi_{2700}(1481,\cdot)\) \(\chi_{2700}(1541,\cdot)\) \(\chi_{2700}(1661,\cdot)\) \(\chi_{2700}(1721,\cdot)\) \(\chi_{2700}(1841,\cdot)\) \(\chi_{2700}(2021,\cdot)\) \(\chi_{2700}(2081,\cdot)\) \(\chi_{2700}(2261,\cdot)\) \(\chi_{2700}(2381,\cdot)\) \(\chi_{2700}(2441,\cdot)\) \(\chi_{2700}(2561,\cdot)\) \(\chi_{2700}(2621,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1351,1001,2377)\) → \((1,e\left(\frac{17}{18}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2700 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{77}{90}\right)\) |