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 \(\chi_{675}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2700.cp
\(\chi_{2700}(29,\cdot)\) \(\chi_{2700}(209,\cdot)\) \(\chi_{2700}(329,\cdot)\) \(\chi_{2700}(389,\cdot)\) \(\chi_{2700}(509,\cdot)\) \(\chi_{2700}(569,\cdot)\) \(\chi_{2700}(689,\cdot)\) \(\chi_{2700}(869,\cdot)\) \(\chi_{2700}(929,\cdot)\) \(\chi_{2700}(1109,\cdot)\) \(\chi_{2700}(1229,\cdot)\) \(\chi_{2700}(1289,\cdot)\) \(\chi_{2700}(1409,\cdot)\) \(\chi_{2700}(1469,\cdot)\) \(\chi_{2700}(1589,\cdot)\) \(\chi_{2700}(1769,\cdot)\) \(\chi_{2700}(1829,\cdot)\) \(\chi_{2700}(2009,\cdot)\) \(\chi_{2700}(2129,\cdot)\) \(\chi_{2700}(2189,\cdot)\) \(\chi_{2700}(2309,\cdot)\) \(\chi_{2700}(2369,\cdot)\) \(\chi_{2700}(2489,\cdot)\) \(\chi_{2700}(2669,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1351,1001,2377)\) → \((1,e\left(\frac{1}{18}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2700 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{31}{90}\right)\) |