Basic properties
| Modulus: | \(3006\) | |
| Conductor: | \(1503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(498\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1503}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3006.p
\(\chi_{3006}(5,\cdot)\) \(\chi_{3006}(23,\cdot)\) \(\chi_{3006}(41,\cdot)\) \(\chi_{3006}(59,\cdot)\) \(\chi_{3006}(83,\cdot)\) \(\chi_{3006}(95,\cdot)\) \(\chi_{3006}(101,\cdot)\) \(\chi_{3006}(113,\cdot)\) \(\chi_{3006}(119,\cdot)\) \(\chi_{3006}(131,\cdot)\) \(\chi_{3006}(149,\cdot)\) \(\chi_{3006}(155,\cdot)\) \(\chi_{3006}(227,\cdot)\) \(\chi_{3006}(245,\cdot)\) \(\chi_{3006}(257,\cdot)\) \(\chi_{3006}(347,\cdot)\) \(\chi_{3006}(371,\cdot)\) \(\chi_{3006}(389,\cdot)\) \(\chi_{3006}(401,\cdot)\) \(\chi_{3006}(407,\cdot)\) \(\chi_{3006}(425,\cdot)\) \(\chi_{3006}(437,\cdot)\) \(\chi_{3006}(443,\cdot)\) \(\chi_{3006}(473,\cdot)\) \(\chi_{3006}(479,\cdot)\) \(\chi_{3006}(497,\cdot)\) \(\chi_{3006}(527,\cdot)\) \(\chi_{3006}(569,\cdot)\) \(\chi_{3006}(581,\cdot)\) \(\chi_{3006}(587,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((335,1675)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3006 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{249}\right)\) | \(e\left(\frac{11}{249}\right)\) | \(e\left(\frac{1}{498}\right)\) | \(e\left(\frac{143}{498}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{29}{83}\right)\) | \(e\left(\frac{190}{249}\right)\) | \(e\left(\frac{86}{249}\right)\) | \(e\left(\frac{367}{498}\right)\) | \(e\left(\frac{52}{249}\right)\) |