Basic properties
Modulus: | \(3456\) | |
Conductor: | \(1728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1728}(1381,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3456.cm
\(\chi_{3456}(25,\cdot)\) \(\chi_{3456}(121,\cdot)\) \(\chi_{3456}(169,\cdot)\) \(\chi_{3456}(265,\cdot)\) \(\chi_{3456}(313,\cdot)\) \(\chi_{3456}(409,\cdot)\) \(\chi_{3456}(457,\cdot)\) \(\chi_{3456}(553,\cdot)\) \(\chi_{3456}(601,\cdot)\) \(\chi_{3456}(697,\cdot)\) \(\chi_{3456}(745,\cdot)\) \(\chi_{3456}(841,\cdot)\) \(\chi_{3456}(889,\cdot)\) \(\chi_{3456}(985,\cdot)\) \(\chi_{3456}(1033,\cdot)\) \(\chi_{3456}(1129,\cdot)\) \(\chi_{3456}(1177,\cdot)\) \(\chi_{3456}(1273,\cdot)\) \(\chi_{3456}(1321,\cdot)\) \(\chi_{3456}(1417,\cdot)\) \(\chi_{3456}(1465,\cdot)\) \(\chi_{3456}(1561,\cdot)\) \(\chi_{3456}(1609,\cdot)\) \(\chi_{3456}(1705,\cdot)\) \(\chi_{3456}(1753,\cdot)\) \(\chi_{3456}(1849,\cdot)\) \(\chi_{3456}(1897,\cdot)\) \(\chi_{3456}(1993,\cdot)\) \(\chi_{3456}(2041,\cdot)\) \(\chi_{3456}(2137,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{144})$ |
Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2431,2053,2945)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 3456 }(2137, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{144}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{37}{144}\right)\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{43}{144}\right)\) | \(e\left(\frac{13}{18}\right)\) |