Basic properties
| Modulus: | \(4010\) | |
| Conductor: | \(401\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{401}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4010.cb
\(\chi_{4010}(21,\cdot)\) \(\chi_{4010}(31,\cdot)\) \(\chi_{4010}(61,\cdot)\) \(\chi_{4010}(71,\cdot)\) \(\chi_{4010}(91,\cdot)\) \(\chi_{4010}(101,\cdot)\) \(\chi_{4010}(131,\cdot)\) \(\chi_{4010}(141,\cdot)\) \(\chi_{4010}(161,\cdot)\) \(\chi_{4010}(191,\cdot)\) \(\chi_{4010}(211,\cdot)\) \(\chi_{4010}(231,\cdot)\) \(\chi_{4010}(251,\cdot)\) \(\chi_{4010}(271,\cdot)\) \(\chi_{4010}(281,\cdot)\) \(\chi_{4010}(341,\cdot)\) \(\chi_{4010}(461,\cdot)\) \(\chi_{4010}(521,\cdot)\) \(\chi_{4010}(531,\cdot)\) \(\chi_{4010}(551,\cdot)\) \(\chi_{4010}(571,\cdot)\) \(\chi_{4010}(591,\cdot)\) \(\chi_{4010}(611,\cdot)\) \(\chi_{4010}(641,\cdot)\) \(\chi_{4010}(661,\cdot)\) \(\chi_{4010}(671,\cdot)\) \(\chi_{4010}(701,\cdot)\) \(\chi_{4010}(711,\cdot)\) \(\chi_{4010}(731,\cdot)\) \(\chi_{4010}(741,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((2407,3211)\) → \((1,e\left(\frac{69}{400}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4010 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{400}\right)\) | \(e\left(\frac{139}{200}\right)\) | \(e\left(\frac{69}{200}\right)\) | \(e\left(\frac{93}{200}\right)\) | \(e\left(\frac{11}{400}\right)\) | \(e\left(\frac{27}{400}\right)\) | \(e\left(\frac{47}{400}\right)\) | \(e\left(\frac{347}{400}\right)\) | \(e\left(\frac{79}{400}\right)\) | \(e\left(\frac{207}{400}\right)\) |