Basic properties
Modulus: | \(5166\) | |
Conductor: | \(2583\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2583}(229,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5166.fq
\(\chi_{5166}(229,\cdot)\) \(\chi_{5166}(481,\cdot)\) \(\chi_{5166}(745,\cdot)\) \(\chi_{5166}(997,\cdot)\) \(\chi_{5166}(1237,\cdot)\) \(\chi_{5166}(1249,\cdot)\) \(\chi_{5166}(1375,\cdot)\) \(\chi_{5166}(1489,\cdot)\) \(\chi_{5166}(1627,\cdot)\) \(\chi_{5166}(1741,\cdot)\) \(\chi_{5166}(1867,\cdot)\) \(\chi_{5166}(1879,\cdot)\) \(\chi_{5166}(2119,\cdot)\) \(\chi_{5166}(2371,\cdot)\) \(\chi_{5166}(2635,\cdot)\) \(\chi_{5166}(2887,\cdot)\) \(\chi_{5166}(3127,\cdot)\) \(\chi_{5166}(3265,\cdot)\) \(\chi_{5166}(3379,\cdot)\) \(\chi_{5166}(3391,\cdot)\) \(\chi_{5166}(3643,\cdot)\) \(\chi_{5166}(3757,\cdot)\) \(\chi_{5166}(3883,\cdot)\) \(\chi_{5166}(4135,\cdot)\) \(\chi_{5166}(4147,\cdot)\) \(\chi_{5166}(4399,\cdot)\) \(\chi_{5166}(4525,\cdot)\) \(\chi_{5166}(4639,\cdot)\) \(\chi_{5166}(4891,\cdot)\) \(\chi_{5166}(4903,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,3655)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{13}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 5166 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) |