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 \(\chi_{1127}(958,\cdot)\) | 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)
|
Galois orbit 3381.cd
\(\chi_{3381}(34,\cdot)\) \(\chi_{3381}(76,\cdot)\) \(\chi_{3381}(181,\cdot)\) \(\chi_{3381}(286,\cdot)\) \(\chi_{3381}(412,\cdot)\) \(\chi_{3381}(433,\cdot)\) \(\chi_{3381}(454,\cdot)\) \(\chi_{3381}(475,\cdot)\) \(\chi_{3381}(517,\cdot)\) \(\chi_{3381}(559,\cdot)\) \(\chi_{3381}(580,\cdot)\) \(\chi_{3381}(664,\cdot)\) \(\chi_{3381}(727,\cdot)\) \(\chi_{3381}(769,\cdot)\) \(\chi_{3381}(895,\cdot)\) \(\chi_{3381}(916,\cdot)\) \(\chi_{3381}(937,\cdot)\) \(\chi_{3381}(958,\cdot)\) \(\chi_{3381}(1000,\cdot)\) \(\chi_{3381}(1042,\cdot)\) \(\chi_{3381}(1063,\cdot)\) \(\chi_{3381}(1147,\cdot)\) \(\chi_{3381}(1210,\cdot)\) \(\chi_{3381}(1252,\cdot)\) \(\chi_{3381}(1378,\cdot)\) \(\chi_{3381}(1399,\cdot)\) \(\chi_{3381}(1441,\cdot)\) \(\chi_{3381}(1483,\cdot)\) \(\chi_{3381}(1525,\cdot)\) \(\chi_{3381}(1546,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((1,e\left(\frac{1}{14}\right),e\left(\frac{17}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(958, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{1}{11}\right)\) |