Basic properties
| Modulus: | \(3004\) | |
| Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(75\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{751}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3004.u
\(\chi_{3004}(61,\cdot)\) \(\chi_{3004}(121,\cdot)\) \(\chi_{3004}(197,\cdot)\) \(\chi_{3004}(229,\cdot)\) \(\chi_{3004}(273,\cdot)\) \(\chi_{3004}(405,\cdot)\) \(\chi_{3004}(637,\cdot)\) \(\chi_{3004}(717,\cdot)\) \(\chi_{3004}(837,\cdot)\) \(\chi_{3004}(881,\cdot)\) \(\chi_{3004}(941,\cdot)\) \(\chi_{3004}(945,\cdot)\) \(\chi_{3004}(1125,\cdot)\) \(\chi_{3004}(1129,\cdot)\) \(\chi_{3004}(1373,\cdot)\) \(\chi_{3004}(1609,\cdot)\) \(\chi_{3004}(1621,\cdot)\) \(\chi_{3004}(1633,\cdot)\) \(\chi_{3004}(1665,\cdot)\) \(\chi_{3004}(1801,\cdot)\) \(\chi_{3004}(1809,\cdot)\) \(\chi_{3004}(1901,\cdot)\) \(\chi_{3004}(1953,\cdot)\) \(\chi_{3004}(1973,\cdot)\) \(\chi_{3004}(2133,\cdot)\) \(\chi_{3004}(2141,\cdot)\) \(\chi_{3004}(2145,\cdot)\) \(\chi_{3004}(2285,\cdot)\) \(\chi_{3004}(2305,\cdot)\) \(\chi_{3004}(2433,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\((1503,1505)\) → \((1,e\left(\frac{56}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3004 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{37}{75}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{23}{75}\right)\) | \(e\left(\frac{22}{75}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{62}{75}\right)\) |