Basic properties
Modulus: | \(1350\) | |
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 \(\chi_{675}(421,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1350.bc
\(\chi_{1350}(31,\cdot)\) \(\chi_{1350}(61,\cdot)\) \(\chi_{1350}(121,\cdot)\) \(\chi_{1350}(211,\cdot)\) \(\chi_{1350}(241,\cdot)\) \(\chi_{1350}(331,\cdot)\) \(\chi_{1350}(391,\cdot)\) \(\chi_{1350}(421,\cdot)\) \(\chi_{1350}(481,\cdot)\) \(\chi_{1350}(511,\cdot)\) \(\chi_{1350}(571,\cdot)\) \(\chi_{1350}(661,\cdot)\) \(\chi_{1350}(691,\cdot)\) \(\chi_{1350}(781,\cdot)\) \(\chi_{1350}(841,\cdot)\) \(\chi_{1350}(871,\cdot)\) \(\chi_{1350}(931,\cdot)\) \(\chi_{1350}(961,\cdot)\) \(\chi_{1350}(1021,\cdot)\) \(\chi_{1350}(1111,\cdot)\) \(\chi_{1350}(1141,\cdot)\) \(\chi_{1350}(1231,\cdot)\) \(\chi_{1350}(1291,\cdot)\) \(\chi_{1350}(1321,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1001,1027)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 1350 }(421, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) |