Basic properties
| Modulus: | \(119952\) | |
| Conductor: | \(6664\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{6664}(3405,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 119952.cag
\(\chi_{119952}(73,\cdot)\) \(\chi_{119952}(649,\cdot)\) \(\chi_{119952}(1081,\cdot)\) \(\chi_{119952}(3097,\cdot)\) \(\chi_{119952}(4681,\cdot)\) \(\chi_{119952}(5689,\cdot)\) \(\chi_{119952}(7129,\cdot)\) \(\chi_{119952}(8137,\cdot)\) \(\chi_{119952}(11737,\cdot)\) \(\chi_{119952}(12169,\cdot)\) \(\chi_{119952}(12745,\cdot)\) \(\chi_{119952}(14185,\cdot)\) \(\chi_{119952}(14761,\cdot)\) \(\chi_{119952}(15193,\cdot)\) \(\chi_{119952}(15769,\cdot)\) \(\chi_{119952}(17209,\cdot)\) \(\chi_{119952}(17785,\cdot)\) \(\chi_{119952}(18217,\cdot)\) \(\chi_{119952}(20233,\cdot)\) \(\chi_{119952}(21817,\cdot)\) \(\chi_{119952}(22825,\cdot)\) \(\chi_{119952}(24265,\cdot)\) \(\chi_{119952}(25273,\cdot)\) \(\chi_{119952}(26857,\cdot)\) \(\chi_{119952}(28873,\cdot)\) \(\chi_{119952}(29305,\cdot)\) \(\chi_{119952}(29881,\cdot)\) \(\chi_{119952}(31321,\cdot)\) \(\chi_{119952}(31897,\cdot)\) \(\chi_{119952}(32329,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((104959,29989,106625,117505,14113)\) → \((1,-1,1,e\left(\frac{37}{42}\right),e\left(\frac{5}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 119952 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{205}{336}\right)\) | \(e\left(\frac{311}{336}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{55}{336}\right)\) | \(e\left(\frac{37}{168}\right)\) | \(e\left(\frac{47}{112}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{1}{336}\right)\) | \(e\left(\frac{73}{112}\right)\) |