Basic properties
Modulus: | \(9200\) | |
Conductor: | \(2300\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2300}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9200.fq
\(\chi_{9200}(127,\cdot)\) \(\chi_{9200}(223,\cdot)\) \(\chi_{9200}(303,\cdot)\) \(\chi_{9200}(463,\cdot)\) \(\chi_{9200}(623,\cdot)\) \(\chi_{9200}(703,\cdot)\) \(\chi_{9200}(767,\cdot)\) \(\chi_{9200}(863,\cdot)\) \(\chi_{9200}(1087,\cdot)\) \(\chi_{9200}(1327,\cdot)\) \(\chi_{9200}(1503,\cdot)\) \(\chi_{9200}(1567,\cdot)\) \(\chi_{9200}(1727,\cdot)\) \(\chi_{9200}(1823,\cdot)\) \(\chi_{9200}(1967,\cdot)\) \(\chi_{9200}(2063,\cdot)\) \(\chi_{9200}(2303,\cdot)\) \(\chi_{9200}(2447,\cdot)\) \(\chi_{9200}(2463,\cdot)\) \(\chi_{9200}(2703,\cdot)\) \(\chi_{9200}(2847,\cdot)\) \(\chi_{9200}(2927,\cdot)\) \(\chi_{9200}(3167,\cdot)\) \(\chi_{9200}(3183,\cdot)\) \(\chi_{9200}(3247,\cdot)\) \(\chi_{9200}(3567,\cdot)\) \(\chi_{9200}(3583,\cdot)\) \(\chi_{9200}(3647,\cdot)\) \(\chi_{9200}(3663,\cdot)\) \(\chi_{9200}(3903,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((-1,1,e\left(\frac{7}{20}\right),e\left(\frac{8}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 9200 }(2303, a) \) | \(1\) | \(1\) | \(e\left(\frac{129}{220}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{183}{220}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{87}{110}\right)\) |