Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(5915\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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.en
\(\chi_{5915}(272,\cdot)\) \(\chi_{5915}(363,\cdot)\) \(\chi_{5915}(727,\cdot)\) \(\chi_{5915}(818,\cdot)\) \(\chi_{5915}(1273,\cdot)\) \(\chi_{5915}(1637,\cdot)\) \(\chi_{5915}(1728,\cdot)\) \(\chi_{5915}(2092,\cdot)\) \(\chi_{5915}(2183,\cdot)\) \(\chi_{5915}(2547,\cdot)\) \(\chi_{5915}(2638,\cdot)\) \(\chi_{5915}(3002,\cdot)\) \(\chi_{5915}(3093,\cdot)\) \(\chi_{5915}(3457,\cdot)\) \(\chi_{5915}(3912,\cdot)\) \(\chi_{5915}(4003,\cdot)\) \(\chi_{5915}(4367,\cdot)\) \(\chi_{5915}(4458,\cdot)\) \(\chi_{5915}(4822,\cdot)\) \(\chi_{5915}(4913,\cdot)\) \(\chi_{5915}(5277,\cdot)\) \(\chi_{5915}(5368,\cdot)\) \(\chi_{5915}(5732,\cdot)\) \(\chi_{5915}(5823,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,5071,1016)\) → \((i,-1,e\left(\frac{25}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(272, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{7}{52}\right)\) |