Basic properties
Modulus: | \(3450\) | |
Conductor: | \(1725\) | 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 \(\chi_{1725}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3450.bn
\(\chi_{3450}(89,\cdot)\) \(\chi_{3450}(329,\cdot)\) \(\chi_{3450}(359,\cdot)\) \(\chi_{3450}(389,\cdot)\) \(\chi_{3450}(419,\cdot)\) \(\chi_{3450}(479,\cdot)\) \(\chi_{3450}(539,\cdot)\) \(\chi_{3450}(569,\cdot)\) \(\chi_{3450}(659,\cdot)\) \(\chi_{3450}(779,\cdot)\) \(\chi_{3450}(839,\cdot)\) \(\chi_{3450}(1019,\cdot)\) \(\chi_{3450}(1079,\cdot)\) \(\chi_{3450}(1109,\cdot)\) \(\chi_{3450}(1169,\cdot)\) \(\chi_{3450}(1229,\cdot)\) \(\chi_{3450}(1259,\cdot)\) \(\chi_{3450}(1469,\cdot)\) \(\chi_{3450}(1529,\cdot)\) \(\chi_{3450}(1709,\cdot)\) \(\chi_{3450}(1739,\cdot)\) \(\chi_{3450}(1769,\cdot)\) \(\chi_{3450}(1859,\cdot)\) \(\chi_{3450}(1919,\cdot)\) \(\chi_{3450}(2039,\cdot)\) \(\chi_{3450}(2159,\cdot)\) \(\chi_{3450}(2219,\cdot)\) \(\chi_{3450}(2429,\cdot)\) \(\chi_{3450}(2459,\cdot)\) \(\chi_{3450}(2489,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1151,277,1201)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{5}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3450 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{7}{11}\right)\) |