Basic properties
| Modulus: | \(8046\) | |
| Conductor: | \(149\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(37\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{149}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8046.s
\(\chi_{8046}(379,\cdot)\) \(\chi_{8046}(703,\cdot)\) \(\chi_{8046}(919,\cdot)\) \(\chi_{8046}(1675,\cdot)\) \(\chi_{8046}(1837,\cdot)\) \(\chi_{8046}(2215,\cdot)\) \(\chi_{8046}(2323,\cdot)\) \(\chi_{8046}(2377,\cdot)\) \(\chi_{8046}(2539,\cdot)\) \(\chi_{8046}(2647,\cdot)\) \(\chi_{8046}(2701,\cdot)\) \(\chi_{8046}(2755,\cdot)\) \(\chi_{8046}(2809,\cdot)\) \(\chi_{8046}(2971,\cdot)\) \(\chi_{8046}(3295,\cdot)\) \(\chi_{8046}(3403,\cdot)\) \(\chi_{8046}(3457,\cdot)\) \(\chi_{8046}(3997,\cdot)\) \(\chi_{8046}(4051,\cdot)\) \(\chi_{8046}(4267,\cdot)\) \(\chi_{8046}(4537,\cdot)\) \(\chi_{8046}(4699,\cdot)\) \(\chi_{8046}(4807,\cdot)\) \(\chi_{8046}(5401,\cdot)\) \(\chi_{8046}(5509,\cdot)\) \(\chi_{8046}(5617,\cdot)\) \(\chi_{8046}(5725,\cdot)\) \(\chi_{8046}(6211,\cdot)\) \(\chi_{8046}(6589,\cdot)\) \(\chi_{8046}(6751,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 37 polynomial |
Values on generators
\((299,3727)\) → \((1,e\left(\frac{13}{37}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8046 }(379, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{23}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{14}{37}\right)\) |