Basic properties
| Modulus: | \(3648\) | |
| Conductor: | \(3648\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 3648.ei
\(\chi_{3648}(29,\cdot)\) \(\chi_{3648}(53,\cdot)\) \(\chi_{3648}(173,\cdot)\) \(\chi_{3648}(269,\cdot)\) \(\chi_{3648}(317,\cdot)\) \(\chi_{3648}(413,\cdot)\) \(\chi_{3648}(485,\cdot)\) \(\chi_{3648}(509,\cdot)\) \(\chi_{3648}(629,\cdot)\) \(\chi_{3648}(725,\cdot)\) \(\chi_{3648}(773,\cdot)\) \(\chi_{3648}(869,\cdot)\) \(\chi_{3648}(941,\cdot)\) \(\chi_{3648}(965,\cdot)\) \(\chi_{3648}(1085,\cdot)\) \(\chi_{3648}(1181,\cdot)\) \(\chi_{3648}(1229,\cdot)\) \(\chi_{3648}(1325,\cdot)\) \(\chi_{3648}(1397,\cdot)\) \(\chi_{3648}(1421,\cdot)\) \(\chi_{3648}(1541,\cdot)\) \(\chi_{3648}(1637,\cdot)\) \(\chi_{3648}(1685,\cdot)\) \(\chi_{3648}(1781,\cdot)\) \(\chi_{3648}(1853,\cdot)\) \(\chi_{3648}(1877,\cdot)\) \(\chi_{3648}(1997,\cdot)\) \(\chi_{3648}(2093,\cdot)\) \(\chi_{3648}(2141,\cdot)\) \(\chi_{3648}(2237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2623,2053,1217,1921)\) → \((1,e\left(\frac{11}{16}\right),-1,e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3648 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{144}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{5}{144}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{17}{144}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{121}{144}\right)\) |