Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(42,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.eh
\(\chi_{5915}(211,\cdot)\) \(\chi_{5915}(386,\cdot)\) \(\chi_{5915}(666,\cdot)\) \(\chi_{5915}(841,\cdot)\) \(\chi_{5915}(1121,\cdot)\) \(\chi_{5915}(1296,\cdot)\) \(\chi_{5915}(1576,\cdot)\) \(\chi_{5915}(1751,\cdot)\) \(\chi_{5915}(2031,\cdot)\) \(\chi_{5915}(2206,\cdot)\) \(\chi_{5915}(2486,\cdot)\) \(\chi_{5915}(2661,\cdot)\) \(\chi_{5915}(2941,\cdot)\) \(\chi_{5915}(3116,\cdot)\) \(\chi_{5915}(3396,\cdot)\) \(\chi_{5915}(3851,\cdot)\) \(\chi_{5915}(4026,\cdot)\) \(\chi_{5915}(4306,\cdot)\) \(\chi_{5915}(4481,\cdot)\) \(\chi_{5915}(4761,\cdot)\) \(\chi_{5915}(4936,\cdot)\) \(\chi_{5915}(5391,\cdot)\) \(\chi_{5915}(5671,\cdot)\) \(\chi_{5915}(5846,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((2367,5071,1016)\) → \((1,1,e\left(\frac{19}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(211, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) |