Basic properties
| Modulus: | \(5915\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.ei
\(\chi_{5915}(8,\cdot)\) \(\chi_{5915}(57,\cdot)\) \(\chi_{5915}(463,\cdot)\) \(\chi_{5915}(512,\cdot)\) \(\chi_{5915}(918,\cdot)\) \(\chi_{5915}(967,\cdot)\) \(\chi_{5915}(1373,\cdot)\) \(\chi_{5915}(1828,\cdot)\) \(\chi_{5915}(1877,\cdot)\) \(\chi_{5915}(2283,\cdot)\) \(\chi_{5915}(2332,\cdot)\) \(\chi_{5915}(2738,\cdot)\) \(\chi_{5915}(2787,\cdot)\) \(\chi_{5915}(3193,\cdot)\) \(\chi_{5915}(3242,\cdot)\) \(\chi_{5915}(3697,\cdot)\) \(\chi_{5915}(4103,\cdot)\) \(\chi_{5915}(4152,\cdot)\) \(\chi_{5915}(4558,\cdot)\) \(\chi_{5915}(4607,\cdot)\) \(\chi_{5915}(5013,\cdot)\) \(\chi_{5915}(5062,\cdot)\) \(\chi_{5915}(5468,\cdot)\) \(\chi_{5915}(5517,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,5071,1016)\) → \((-i,1,e\left(\frac{1}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
| \( \chi_{ 5915 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{29}{52}\right)\) |