Basic properties
Modulus: | \(3381\) | |
Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1127}(328,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.cc
\(\chi_{3381}(13,\cdot)\) \(\chi_{3381}(55,\cdot)\) \(\chi_{3381}(118,\cdot)\) \(\chi_{3381}(202,\cdot)\) \(\chi_{3381}(223,\cdot)\) \(\chi_{3381}(265,\cdot)\) \(\chi_{3381}(307,\cdot)\) \(\chi_{3381}(328,\cdot)\) \(\chi_{3381}(349,\cdot)\) \(\chi_{3381}(370,\cdot)\) \(\chi_{3381}(496,\cdot)\) \(\chi_{3381}(601,\cdot)\) \(\chi_{3381}(706,\cdot)\) \(\chi_{3381}(748,\cdot)\) \(\chi_{3381}(790,\cdot)\) \(\chi_{3381}(811,\cdot)\) \(\chi_{3381}(853,\cdot)\) \(\chi_{3381}(1021,\cdot)\) \(\chi_{3381}(1084,\cdot)\) \(\chi_{3381}(1168,\cdot)\) \(\chi_{3381}(1189,\cdot)\) \(\chi_{3381}(1231,\cdot)\) \(\chi_{3381}(1294,\cdot)\) \(\chi_{3381}(1315,\cdot)\) \(\chi_{3381}(1336,\cdot)\) \(\chi_{3381}(1462,\cdot)\) \(\chi_{3381}(1504,\cdot)\) \(\chi_{3381}(1651,\cdot)\) \(\chi_{3381}(1672,\cdot)\) \(\chi_{3381}(1756,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((1,e\left(\frac{3}{14}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(328, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{17}{22}\right)\) |