Basic properties
| Modulus: | \(5166\) | |
| Conductor: | \(861\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{861}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5166.fy
\(\chi_{5166}(53,\cdot)\) \(\chi_{5166}(179,\cdot)\) \(\chi_{5166}(233,\cdot)\) \(\chi_{5166}(485,\cdot)\) \(\chi_{5166}(557,\cdot)\) \(\chi_{5166}(809,\cdot)\) \(\chi_{5166}(1241,\cdot)\) \(\chi_{5166}(1493,\cdot)\) \(\chi_{5166}(1565,\cdot)\) \(\chi_{5166}(1817,\cdot)\) \(\chi_{5166}(1871,\cdot)\) \(\chi_{5166}(1997,\cdot)\) \(\chi_{5166}(2069,\cdot)\) \(\chi_{5166}(2195,\cdot)\) \(\chi_{5166}(2249,\cdot)\) \(\chi_{5166}(2447,\cdot)\) \(\chi_{5166}(2699,\cdot)\) \(\chi_{5166}(2753,\cdot)\) \(\chi_{5166}(3005,\cdot)\) \(\chi_{5166}(3131,\cdot)\) \(\chi_{5166}(3455,\cdot)\) \(\chi_{5166}(3509,\cdot)\) \(\chi_{5166}(3707,\cdot)\) \(\chi_{5166}(3761,\cdot)\) \(\chi_{5166}(4085,\cdot)\) \(\chi_{5166}(4211,\cdot)\) \(\chi_{5166}(4463,\cdot)\) \(\chi_{5166}(4517,\cdot)\) \(\chi_{5166}(4769,\cdot)\) \(\chi_{5166}(4967,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,3655)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{27}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5166 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) |