Basic properties
Modulus: | \(4600\) | |
Conductor: | \(4600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(110\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 4600.cz
\(\chi_{4600}(19,\cdot)\) \(\chi_{4600}(339,\cdot)\) \(\chi_{4600}(379,\cdot)\) \(\chi_{4600}(419,\cdot)\) \(\chi_{4600}(539,\cdot)\) \(\chi_{4600}(619,\cdot)\) \(\chi_{4600}(659,\cdot)\) \(\chi_{4600}(779,\cdot)\) \(\chi_{4600}(819,\cdot)\) \(\chi_{4600}(939,\cdot)\) \(\chi_{4600}(1019,\cdot)\) \(\chi_{4600}(1259,\cdot)\) \(\chi_{4600}(1339,\cdot)\) \(\chi_{4600}(1459,\cdot)\) \(\chi_{4600}(1539,\cdot)\) \(\chi_{4600}(1579,\cdot)\) \(\chi_{4600}(1739,\cdot)\) \(\chi_{4600}(1859,\cdot)\) \(\chi_{4600}(1939,\cdot)\) \(\chi_{4600}(2179,\cdot)\) \(\chi_{4600}(2219,\cdot)\) \(\chi_{4600}(2259,\cdot)\) \(\chi_{4600}(2379,\cdot)\) \(\chi_{4600}(2459,\cdot)\) \(\chi_{4600}(2619,\cdot)\) \(\chi_{4600}(2659,\cdot)\) \(\chi_{4600}(2779,\cdot)\) \(\chi_{4600}(2859,\cdot)\) \(\chi_{4600}(3139,\cdot)\) \(\chi_{4600}(3179,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,2301,2577,1201)\) → \((-1,-1,e\left(\frac{9}{10}\right),e\left(\frac{15}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 4600 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) |