Basic properties
Modulus: | \(9200\) | |
Conductor: | \(4600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4600}(3331,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9200.ez
\(\chi_{9200}(471,\cdot)\) \(\chi_{9200}(631,\cdot)\) \(\chi_{9200}(711,\cdot)\) \(\chi_{9200}(871,\cdot)\) \(\chi_{9200}(1031,\cdot)\) \(\chi_{9200}(1111,\cdot)\) \(\chi_{9200}(1431,\cdot)\) \(\chi_{9200}(1671,\cdot)\) \(\chi_{9200}(1831,\cdot)\) \(\chi_{9200}(2311,\cdot)\) \(\chi_{9200}(2471,\cdot)\) \(\chi_{9200}(2711,\cdot)\) \(\chi_{9200}(2871,\cdot)\) \(\chi_{9200}(3191,\cdot)\) \(\chi_{9200}(3271,\cdot)\) \(\chi_{9200}(3511,\cdot)\) \(\chi_{9200}(3671,\cdot)\) \(\chi_{9200}(4311,\cdot)\) \(\chi_{9200}(4391,\cdot)\) \(\chi_{9200}(4711,\cdot)\) \(\chi_{9200}(4791,\cdot)\) \(\chi_{9200}(5031,\cdot)\) \(\chi_{9200}(5111,\cdot)\) \(\chi_{9200}(5511,\cdot)\) \(\chi_{9200}(5991,\cdot)\) \(\chi_{9200}(6231,\cdot)\) \(\chi_{9200}(6391,\cdot)\) \(\chi_{9200}(6631,\cdot)\) \(\chi_{9200}(6871,\cdot)\) \(\chi_{9200}(7191,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,6901,2577,1201)\) → \((-1,-1,e\left(\frac{2}{5}\right),e\left(\frac{15}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 9200 }(1031, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) |