Basic properties
Modulus: | \(4010\) | |
Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(400\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2005}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4010.bz
\(\chi_{4010}(13,\cdot)\) \(\chi_{4010}(23,\cdot)\) \(\chi_{4010}(37,\cdot)\) \(\chi_{4010}(67,\cdot)\) \(\chi_{4010}(87,\cdot)\) \(\chi_{4010}(117,\cdot)\) \(\chi_{4010}(137,\cdot)\) \(\chi_{4010}(163,\cdot)\) \(\chi_{4010}(187,\cdot)\) \(\chi_{4010}(193,\cdot)\) \(\chi_{4010}(207,\cdot)\) \(\chi_{4010}(217,\cdot)\) \(\chi_{4010}(297,\cdot)\) \(\chi_{4010}(347,\cdot)\) \(\chi_{4010}(367,\cdot)\) \(\chi_{4010}(447,\cdot)\) \(\chi_{4010}(453,\cdot)\) \(\chi_{4010}(467,\cdot)\) \(\chi_{4010}(493,\cdot)\) \(\chi_{4010}(533,\cdot)\) \(\chi_{4010}(537,\cdot)\) \(\chi_{4010}(583,\cdot)\) \(\chi_{4010}(617,\cdot)\) \(\chi_{4010}(663,\cdot)\) \(\chi_{4010}(673,\cdot)\) \(\chi_{4010}(723,\cdot)\) \(\chi_{4010}(727,\cdot)\) \(\chi_{4010}(743,\cdot)\) \(\chi_{4010}(783,\cdot)\) \(\chi_{4010}(787,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{400})$ |
Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((2407,3211)\) → \((-i,e\left(\frac{319}{400}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4010 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{400}\right)\) | \(e\left(\frac{39}{200}\right)\) | \(e\left(\frac{19}{200}\right)\) | \(e\left(\frac{143}{200}\right)\) | \(e\left(\frac{261}{400}\right)\) | \(e\left(\frac{77}{400}\right)\) | \(e\left(\frac{197}{400}\right)\) | \(e\left(\frac{97}{400}\right)\) | \(e\left(\frac{129}{400}\right)\) | \(e\left(\frac{57}{400}\right)\) |