Basic properties
| Modulus: | \(3672\) | |
| Conductor: | \(1836\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1836}(227,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3672.ek
\(\chi_{3672}(23,\cdot)\) \(\chi_{3672}(95,\cdot)\) \(\chi_{3672}(167,\cdot)\) \(\chi_{3672}(311,\cdot)\) \(\chi_{3672}(335,\cdot)\) \(\chi_{3672}(479,\cdot)\) \(\chi_{3672}(551,\cdot)\) \(\chi_{3672}(623,\cdot)\) \(\chi_{3672}(743,\cdot)\) \(\chi_{3672}(839,\cdot)\) \(\chi_{3672}(887,\cdot)\) \(\chi_{3672}(911,\cdot)\) \(\chi_{3672}(959,\cdot)\) \(\chi_{3672}(983,\cdot)\) \(\chi_{3672}(1031,\cdot)\) \(\chi_{3672}(1127,\cdot)\) \(\chi_{3672}(1247,\cdot)\) \(\chi_{3672}(1319,\cdot)\) \(\chi_{3672}(1391,\cdot)\) \(\chi_{3672}(1535,\cdot)\) \(\chi_{3672}(1559,\cdot)\) \(\chi_{3672}(1703,\cdot)\) \(\chi_{3672}(1775,\cdot)\) \(\chi_{3672}(1847,\cdot)\) \(\chi_{3672}(1967,\cdot)\) \(\chi_{3672}(2063,\cdot)\) \(\chi_{3672}(2111,\cdot)\) \(\chi_{3672}(2135,\cdot)\) \(\chi_{3672}(2183,\cdot)\) \(\chi_{3672}(2207,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((919,1837,137,649)\) → \((-1,1,e\left(\frac{13}{18}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3672 }(2063, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{144}\right)\) | \(e\left(\frac{53}{144}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{73}{144}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{131}{144}\right)\) | \(e\left(\frac{55}{144}\right)\) | \(e\left(\frac{2}{3}\right)\) |