Basic properties
Modulus: | \(5915\) | |
Conductor: | \(5915\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.gm
\(\chi_{5915}(12,\cdot)\) \(\chi_{5915}(38,\cdot)\) \(\chi_{5915}(103,\cdot)\) \(\chi_{5915}(402,\cdot)\) \(\chi_{5915}(467,\cdot)\) \(\chi_{5915}(493,\cdot)\) \(\chi_{5915}(558,\cdot)\) \(\chi_{5915}(857,\cdot)\) \(\chi_{5915}(922,\cdot)\) \(\chi_{5915}(948,\cdot)\) \(\chi_{5915}(1312,\cdot)\) \(\chi_{5915}(1377,\cdot)\) \(\chi_{5915}(1403,\cdot)\) \(\chi_{5915}(1468,\cdot)\) \(\chi_{5915}(1767,\cdot)\) \(\chi_{5915}(1832,\cdot)\) \(\chi_{5915}(1923,\cdot)\) \(\chi_{5915}(2222,\cdot)\) \(\chi_{5915}(2287,\cdot)\) \(\chi_{5915}(2313,\cdot)\) \(\chi_{5915}(2378,\cdot)\) \(\chi_{5915}(2677,\cdot)\) \(\chi_{5915}(2742,\cdot)\) \(\chi_{5915}(2768,\cdot)\) \(\chi_{5915}(2833,\cdot)\) \(\chi_{5915}(3132,\cdot)\) \(\chi_{5915}(3197,\cdot)\) \(\chi_{5915}(3223,\cdot)\) \(\chi_{5915}(3288,\cdot)\) \(\chi_{5915}(3587,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,e\left(\frac{5}{6}\right),e\left(\frac{21}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{156}\right)\) |