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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.hm
\(\chi_{5915}(97,\cdot)\) \(\chi_{5915}(132,\cdot)\) \(\chi_{5915}(293,\cdot)\) \(\chi_{5915}(552,\cdot)\) \(\chi_{5915}(713,\cdot)\) \(\chi_{5915}(748,\cdot)\) \(\chi_{5915}(1007,\cdot)\) \(\chi_{5915}(1042,\cdot)\) \(\chi_{5915}(1168,\cdot)\) \(\chi_{5915}(1203,\cdot)\) \(\chi_{5915}(1462,\cdot)\) \(\chi_{5915}(1497,\cdot)\) \(\chi_{5915}(1623,\cdot)\) \(\chi_{5915}(1658,\cdot)\) \(\chi_{5915}(1917,\cdot)\) \(\chi_{5915}(1952,\cdot)\) \(\chi_{5915}(2078,\cdot)\) \(\chi_{5915}(2113,\cdot)\) \(\chi_{5915}(2372,\cdot)\) \(\chi_{5915}(2407,\cdot)\) \(\chi_{5915}(2533,\cdot)\) \(\chi_{5915}(2568,\cdot)\) \(\chi_{5915}(2827,\cdot)\) \(\chi_{5915}(2862,\cdot)\) \(\chi_{5915}(2988,\cdot)\) \(\chi_{5915}(3282,\cdot)\) \(\chi_{5915}(3317,\cdot)\) \(\chi_{5915}(3443,\cdot)\) \(\chi_{5915}(3478,\cdot)\) \(\chi_{5915}(3772,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,-1,e\left(\frac{17}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{103}{156}\right)\) |