Basic properties
| Modulus: | \(87120\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87120.qr
\(\chi_{87120}(721,\cdot)\) \(\chi_{87120}(5761,\cdot)\) \(\chi_{87120}(6481,\cdot)\) \(\chi_{87120}(7201,\cdot)\) \(\chi_{87120}(8641,\cdot)\) \(\chi_{87120}(13681,\cdot)\) \(\chi_{87120}(14401,\cdot)\) \(\chi_{87120}(15121,\cdot)\) \(\chi_{87120}(16561,\cdot)\) \(\chi_{87120}(21601,\cdot)\) \(\chi_{87120}(22321,\cdot)\) \(\chi_{87120}(23041,\cdot)\) \(\chi_{87120}(24481,\cdot)\) \(\chi_{87120}(30961,\cdot)\) \(\chi_{87120}(37441,\cdot)\) \(\chi_{87120}(38161,\cdot)\) \(\chi_{87120}(40321,\cdot)\) \(\chi_{87120}(45361,\cdot)\) \(\chi_{87120}(46081,\cdot)\) \(\chi_{87120}(46801,\cdot)\) \(\chi_{87120}(48241,\cdot)\) \(\chi_{87120}(53281,\cdot)\) \(\chi_{87120}(54001,\cdot)\) \(\chi_{87120}(54721,\cdot)\) \(\chi_{87120}(56161,\cdot)\) \(\chi_{87120}(61201,\cdot)\) \(\chi_{87120}(61921,\cdot)\) \(\chi_{87120}(62641,\cdot)\) \(\chi_{87120}(64081,\cdot)\) \(\chi_{87120}(69121,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((32671,21781,19361,69697,14401)\) → \((1,1,1,1,e\left(\frac{1}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 87120 }(14401, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{5}{22}\right)\) |