Basic properties
| Modulus: | \(6010\) | |
| Conductor: | \(3005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3005}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6010.cw
\(\chi_{6010}(39,\cdot)\) \(\chi_{6010}(49,\cdot)\) \(\chi_{6010}(69,\cdot)\) \(\chi_{6010}(149,\cdot)\) \(\chi_{6010}(209,\cdot)\) \(\chi_{6010}(339,\cdot)\) \(\chi_{6010}(359,\cdot)\) \(\chi_{6010}(479,\cdot)\) \(\chi_{6010}(509,\cdot)\) \(\chi_{6010}(679,\cdot)\) \(\chi_{6010}(699,\cdot)\) \(\chi_{6010}(739,\cdot)\) \(\chi_{6010}(899,\cdot)\) \(\chi_{6010}(909,\cdot)\) \(\chi_{6010}(1069,\cdot)\) \(\chi_{6010}(1089,\cdot)\) \(\chi_{6010}(1179,\cdot)\) \(\chi_{6010}(1279,\cdot)\) \(\chi_{6010}(1319,\cdot)\) \(\chi_{6010}(1619,\cdot)\) \(\chi_{6010}(1849,\cdot)\) \(\chi_{6010}(1959,\cdot)\) \(\chi_{6010}(1999,\cdot)\) \(\chi_{6010}(2029,\cdot)\) \(\chi_{6010}(2069,\cdot)\) \(\chi_{6010}(2169,\cdot)\) \(\chi_{6010}(2269,\cdot)\) \(\chi_{6010}(2389,\cdot)\) \(\chi_{6010}(2419,\cdot)\) \(\chi_{6010}(2539,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((3607,2411)\) → \((-1,e\left(\frac{287}{300}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6010 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{150}\right)\) | \(e\left(\frac{137}{300}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{59}{300}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{167}{300}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{49}{50}\right)\) |