Basic properties
Modulus: | \(5166\) | |
Conductor: | \(287\) | 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 \(\chi_{287}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5166.fu
\(\chi_{5166}(19,\cdot)\) \(\chi_{5166}(145,\cdot)\) \(\chi_{5166}(199,\cdot)\) \(\chi_{5166}(397,\cdot)\) \(\chi_{5166}(649,\cdot)\) \(\chi_{5166}(703,\cdot)\) \(\chi_{5166}(955,\cdot)\) \(\chi_{5166}(1081,\cdot)\) \(\chi_{5166}(1405,\cdot)\) \(\chi_{5166}(1459,\cdot)\) \(\chi_{5166}(1657,\cdot)\) \(\chi_{5166}(1711,\cdot)\) \(\chi_{5166}(2035,\cdot)\) \(\chi_{5166}(2161,\cdot)\) \(\chi_{5166}(2413,\cdot)\) \(\chi_{5166}(2467,\cdot)\) \(\chi_{5166}(2719,\cdot)\) \(\chi_{5166}(2917,\cdot)\) \(\chi_{5166}(2971,\cdot)\) \(\chi_{5166}(3097,\cdot)\) \(\chi_{5166}(3169,\cdot)\) \(\chi_{5166}(3295,\cdot)\) \(\chi_{5166}(3349,\cdot)\) \(\chi_{5166}(3601,\cdot)\) \(\chi_{5166}(3673,\cdot)\) \(\chi_{5166}(3925,\cdot)\) \(\chi_{5166}(4357,\cdot)\) \(\chi_{5166}(4609,\cdot)\) \(\chi_{5166}(4681,\cdot)\) \(\chi_{5166}(4933,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,3655)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{9}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 5166 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) |