Basic properties
Modulus: | \(3344\) | |
Conductor: | \(1672\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1672}(845,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3344.fc
\(\chi_{3344}(9,\cdot)\) \(\chi_{3344}(25,\cdot)\) \(\chi_{3344}(137,\cdot)\) \(\chi_{3344}(169,\cdot)\) \(\chi_{3344}(313,\cdot)\) \(\chi_{3344}(377,\cdot)\) \(\chi_{3344}(537,\cdot)\) \(\chi_{3344}(841,\cdot)\) \(\chi_{3344}(1049,\cdot)\) \(\chi_{3344}(1081,\cdot)\) \(\chi_{3344}(1225,\cdot)\) \(\chi_{3344}(1241,\cdot)\) \(\chi_{3344}(1545,\cdot)\) \(\chi_{3344}(1593,\cdot)\) \(\chi_{3344}(1753,\cdot)\) \(\chi_{3344}(1897,\cdot)\) \(\chi_{3344}(1961,\cdot)\) \(\chi_{3344}(2137,\cdot)\) \(\chi_{3344}(2297,\cdot)\) \(\chi_{3344}(2457,\cdot)\) \(\chi_{3344}(2601,\cdot)\) \(\chi_{3344}(2665,\cdot)\) \(\chi_{3344}(2809,\cdot)\) \(\chi_{3344}(3177,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,837,2433,705)\) → \((1,-1,e\left(\frac{3}{5}\right),e\left(\frac{4}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 3344 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{45}\right)\) |