Basic properties
| Modulus: | \(29040\) | |
| Conductor: | \(1936\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1936}(267,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 29040.me
\(\chi_{29040}(91,\cdot)\) \(\chi_{29040}(691,\cdot)\) \(\chi_{29040}(1171,\cdot)\) \(\chi_{29040}(1411,\cdot)\) \(\chi_{29040}(2011,\cdot)\) \(\chi_{29040}(2491,\cdot)\) \(\chi_{29040}(2611,\cdot)\) \(\chi_{29040}(2731,\cdot)\) \(\chi_{29040}(3331,\cdot)\) \(\chi_{29040}(3811,\cdot)\) \(\chi_{29040}(3931,\cdot)\) \(\chi_{29040}(4051,\cdot)\) \(\chi_{29040}(4651,\cdot)\) \(\chi_{29040}(5131,\cdot)\) \(\chi_{29040}(5251,\cdot)\) \(\chi_{29040}(5371,\cdot)\) \(\chi_{29040}(5971,\cdot)\) \(\chi_{29040}(6451,\cdot)\) \(\chi_{29040}(6571,\cdot)\) \(\chi_{29040}(6691,\cdot)\) \(\chi_{29040}(7291,\cdot)\) \(\chi_{29040}(7891,\cdot)\) \(\chi_{29040}(8011,\cdot)\) \(\chi_{29040}(8611,\cdot)\) \(\chi_{29040}(9091,\cdot)\) \(\chi_{29040}(9211,\cdot)\) \(\chi_{29040}(9331,\cdot)\) \(\chi_{29040}(10411,\cdot)\) \(\chi_{29040}(10531,\cdot)\) \(\chi_{29040}(11251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,21781,19361,11617,14401)\) → \((-1,i,1,1,e\left(\frac{19}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 29040 }(8011, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{137}{220}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{17}{44}\right)\) |