Basic properties
Modulus: | \(7360\) | |
Conductor: | \(7360\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(176\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 7360.fa
\(\chi_{7360}(53,\cdot)\) \(\chi_{7360}(157,\cdot)\) \(\chi_{7360}(237,\cdot)\) \(\chi_{7360}(293,\cdot)\) \(\chi_{7360}(373,\cdot)\) \(\chi_{7360}(477,\cdot)\) \(\chi_{7360}(557,\cdot)\) \(\chi_{7360}(613,\cdot)\) \(\chi_{7360}(773,\cdot)\) \(\chi_{7360}(797,\cdot)\) \(\chi_{7360}(957,\cdot)\) \(\chi_{7360}(1253,\cdot)\) \(\chi_{7360}(1413,\cdot)\) \(\chi_{7360}(1437,\cdot)\) \(\chi_{7360}(1493,\cdot)\) \(\chi_{7360}(1597,\cdot)\) \(\chi_{7360}(1653,\cdot)\) \(\chi_{7360}(1677,\cdot)\) \(\chi_{7360}(1813,\cdot)\) \(\chi_{7360}(1837,\cdot)\) \(\chi_{7360}(1893,\cdot)\) \(\chi_{7360}(1997,\cdot)\) \(\chi_{7360}(2077,\cdot)\) \(\chi_{7360}(2133,\cdot)\) \(\chi_{7360}(2213,\cdot)\) \(\chi_{7360}(2317,\cdot)\) \(\chi_{7360}(2397,\cdot)\) \(\chi_{7360}(2453,\cdot)\) \(\chi_{7360}(2613,\cdot)\) \(\chi_{7360}(2637,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((1151,5061,4417,6721)\) → \((1,e\left(\frac{5}{16}\right),-i,e\left(\frac{19}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 7360 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{176}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{59}{176}\right)\) | \(e\left(\frac{5}{176}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{113}{176}\right)\) | \(e\left(\frac{51}{176}\right)\) | \(e\left(\frac{3}{176}\right)\) | \(e\left(\frac{85}{176}\right)\) |