Basic properties
| Modulus: | \(4010\) | |
| Conductor: | \(401\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(200\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{401}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4010.bu
\(\chi_{4010}(11,\cdot)\) \(\chi_{4010}(111,\cdot)\) \(\chi_{4010}(181,\cdot)\) \(\chi_{4010}(201,\cdot)\) \(\chi_{4010}(221,\cdot)\) \(\chi_{4010}(241,\cdot)\) \(\chi_{4010}(261,\cdot)\) \(\chi_{4010}(351,\cdot)\) \(\chi_{4010}(361,\cdot)\) \(\chi_{4010}(391,\cdot)\) \(\chi_{4010}(411,\cdot)\) \(\chi_{4010}(441,\cdot)\) \(\chi_{4010}(451,\cdot)\) \(\chi_{4010}(541,\cdot)\) \(\chi_{4010}(561,\cdot)\) \(\chi_{4010}(581,\cdot)\) \(\chi_{4010}(601,\cdot)\) \(\chi_{4010}(621,\cdot)\) \(\chi_{4010}(691,\cdot)\) \(\chi_{4010}(791,\cdot)\) \(\chi_{4010}(811,\cdot)\) \(\chi_{4010}(891,\cdot)\) \(\chi_{4010}(911,\cdot)\) \(\chi_{4010}(961,\cdot)\) \(\chi_{4010}(971,\cdot)\) \(\chi_{4010}(1031,\cdot)\) \(\chi_{4010}(1091,\cdot)\) \(\chi_{4010}(1121,\cdot)\) \(\chi_{4010}(1201,\cdot)\) \(\chi_{4010}(1211,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2407,3211)\) → \((1,e\left(\frac{97}{200}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4010 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{200}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{143}{200}\right)\) | \(e\left(\frac{151}{200}\right)\) | \(e\left(\frac{11}{200}\right)\) | \(e\left(\frac{111}{200}\right)\) | \(e\left(\frac{27}{200}\right)\) | \(e\left(\frac{91}{200}\right)\) |