Basic properties
Modulus: | \(3381\) | |
Conductor: | \(3381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.bz
\(\chi_{3381}(41,\cdot)\) \(\chi_{3381}(62,\cdot)\) \(\chi_{3381}(104,\cdot)\) \(\chi_{3381}(167,\cdot)\) \(\chi_{3381}(188,\cdot)\) \(\chi_{3381}(209,\cdot)\) \(\chi_{3381}(335,\cdot)\) \(\chi_{3381}(377,\cdot)\) \(\chi_{3381}(524,\cdot)\) \(\chi_{3381}(545,\cdot)\) \(\chi_{3381}(629,\cdot)\) \(\chi_{3381}(650,\cdot)\) \(\chi_{3381}(671,\cdot)\) \(\chi_{3381}(692,\cdot)\) \(\chi_{3381}(818,\cdot)\) \(\chi_{3381}(860,\cdot)\) \(\chi_{3381}(923,\cdot)\) \(\chi_{3381}(1007,\cdot)\) \(\chi_{3381}(1070,\cdot)\) \(\chi_{3381}(1112,\cdot)\) \(\chi_{3381}(1133,\cdot)\) \(\chi_{3381}(1154,\cdot)\) \(\chi_{3381}(1301,\cdot)\) \(\chi_{3381}(1343,\cdot)\) \(\chi_{3381}(1406,\cdot)\) \(\chi_{3381}(1490,\cdot)\) \(\chi_{3381}(1511,\cdot)\) \(\chi_{3381}(1553,\cdot)\) \(\chi_{3381}(1595,\cdot)\) \(\chi_{3381}(1637,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{3}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(1595, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{109}{154}\right)\) | \(e\left(\frac{115}{154}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{13}{22}\right)\) |