Basic properties
Modulus: | \(2700\) | |
Conductor: | \(2700\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2700.cj
\(\chi_{2700}(79,\cdot)\) \(\chi_{2700}(139,\cdot)\) \(\chi_{2700}(259,\cdot)\) \(\chi_{2700}(319,\cdot)\) \(\chi_{2700}(439,\cdot)\) \(\chi_{2700}(619,\cdot)\) \(\chi_{2700}(679,\cdot)\) \(\chi_{2700}(859,\cdot)\) \(\chi_{2700}(979,\cdot)\) \(\chi_{2700}(1039,\cdot)\) \(\chi_{2700}(1159,\cdot)\) \(\chi_{2700}(1219,\cdot)\) \(\chi_{2700}(1339,\cdot)\) \(\chi_{2700}(1519,\cdot)\) \(\chi_{2700}(1579,\cdot)\) \(\chi_{2700}(1759,\cdot)\) \(\chi_{2700}(1879,\cdot)\) \(\chi_{2700}(1939,\cdot)\) \(\chi_{2700}(2059,\cdot)\) \(\chi_{2700}(2119,\cdot)\) \(\chi_{2700}(2239,\cdot)\) \(\chi_{2700}(2419,\cdot)\) \(\chi_{2700}(2479,\cdot)\) \(\chi_{2700}(2659,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1351,1001,2377)\) → \((-1,e\left(\frac{5}{9}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 2700 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{38}{45}\right)\) |