Basic properties
Modulus: | \(2850\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(396,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.ce
\(\chi_{2850}(61,\cdot)\) \(\chi_{2850}(271,\cdot)\) \(\chi_{2850}(481,\cdot)\) \(\chi_{2850}(511,\cdot)\) \(\chi_{2850}(541,\cdot)\) \(\chi_{2850}(631,\cdot)\) \(\chi_{2850}(841,\cdot)\) \(\chi_{2850}(871,\cdot)\) \(\chi_{2850}(1081,\cdot)\) \(\chi_{2850}(1111,\cdot)\) \(\chi_{2850}(1411,\cdot)\) \(\chi_{2850}(1441,\cdot)\) \(\chi_{2850}(1621,\cdot)\) \(\chi_{2850}(1681,\cdot)\) \(\chi_{2850}(1771,\cdot)\) \(\chi_{2850}(1981,\cdot)\) \(\chi_{2850}(2011,\cdot)\) \(\chi_{2850}(2191,\cdot)\) \(\chi_{2850}(2221,\cdot)\) \(\chi_{2850}(2341,\cdot)\) \(\chi_{2850}(2581,\cdot)\) \(\chi_{2850}(2761,\cdot)\) \(\chi_{2850}(2791,\cdot)\) \(\chi_{2850}(2821,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{2}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 2850 }(871, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{5}{9}\right)\) |