Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(34848\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1320\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{34848}(4397,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.ls
\(\chi_{69696}(41,\cdot)\) \(\chi_{69696}(281,\cdot)\) \(\chi_{69696}(425,\cdot)\) \(\chi_{69696}(569,\cdot)\) \(\chi_{69696}(761,\cdot)\) \(\chi_{69696}(1289,\cdot)\) \(\chi_{69696}(1337,\cdot)\) \(\chi_{69696}(1481,\cdot)\) \(\chi_{69696}(1625,\cdot)\) \(\chi_{69696}(1865,\cdot)\) \(\chi_{69696}(2009,\cdot)\) \(\chi_{69696}(2153,\cdot)\) \(\chi_{69696}(2345,\cdot)\) \(\chi_{69696}(2873,\cdot)\) \(\chi_{69696}(2921,\cdot)\) \(\chi_{69696}(3209,\cdot)\) \(\chi_{69696}(3449,\cdot)\) \(\chi_{69696}(3593,\cdot)\) \(\chi_{69696}(3737,\cdot)\) \(\chi_{69696}(3929,\cdot)\) \(\chi_{69696}(4457,\cdot)\) \(\chi_{69696}(4505,\cdot)\) \(\chi_{69696}(4649,\cdot)\) \(\chi_{69696}(4793,\cdot)\) \(\chi_{69696}(5033,\cdot)\) \(\chi_{69696}(5177,\cdot)\) \(\chi_{69696}(5513,\cdot)\) \(\chi_{69696}(6089,\cdot)\) \(\chi_{69696}(6233,\cdot)\) \(\chi_{69696}(6377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1320})$ |
| Fixed field: | Number field defined by a degree 1320 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{23}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{679}{1320}\right)\) | \(e\left(\frac{361}{660}\right)\) | \(e\left(\frac{1201}{1320}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{211}{440}\right)\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{19}{660}\right)\) | \(e\left(\frac{17}{1320}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{27}{440}\right)\) |