Basic properties
Modulus: | \(6030\) | |
Conductor: | \(335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{335}(98,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6030.ee
\(\chi_{6030}(433,\cdot)\) \(\chi_{6030}(487,\cdot)\) \(\chi_{6030}(577,\cdot)\) \(\chi_{6030}(757,\cdot)\) \(\chi_{6030}(883,\cdot)\) \(\chi_{6030}(1693,\cdot)\) \(\chi_{6030}(1783,\cdot)\) \(\chi_{6030}(1837,\cdot)\) \(\chi_{6030}(1927,\cdot)\) \(\chi_{6030}(1963,\cdot)\) \(\chi_{6030}(2017,\cdot)\) \(\chi_{6030}(2377,\cdot)\) \(\chi_{6030}(2557,\cdot)\) \(\chi_{6030}(2647,\cdot)\) \(\chi_{6030}(2737,\cdot)\) \(\chi_{6030}(2827,\cdot)\) \(\chi_{6030}(3043,\cdot)\) \(\chi_{6030}(3133,\cdot)\) \(\chi_{6030}(3223,\cdot)\) \(\chi_{6030}(3277,\cdot)\) \(\chi_{6030}(3547,\cdot)\) \(\chi_{6030}(3583,\cdot)\) \(\chi_{6030}(3763,\cdot)\) \(\chi_{6030}(3853,\cdot)\) \(\chi_{6030}(3943,\cdot)\) \(\chi_{6030}(3997,\cdot)\) \(\chi_{6030}(4033,\cdot)\) \(\chi_{6030}(4267,\cdot)\) \(\chi_{6030}(4357,\cdot)\) \(\chi_{6030}(4483,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4691,1207,3151)\) → \((1,-i,e\left(\frac{47}{66}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 6030 }(433, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{49}{66}\right)\) |