Basic properties
| Modulus: | \(2368\) | |
| Conductor: | \(1184\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1184}(187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2368.do
\(\chi_{2368}(39,\cdot)\) \(\chi_{2368}(87,\cdot)\) \(\chi_{2368}(135,\cdot)\) \(\chi_{2368}(183,\cdot)\) \(\chi_{2368}(375,\cdot)\) \(\chi_{2368}(503,\cdot)\) \(\chi_{2368}(535,\cdot)\) \(\chi_{2368}(647,\cdot)\) \(\chi_{2368}(759,\cdot)\) \(\chi_{2368}(871,\cdot)\) \(\chi_{2368}(903,\cdot)\) \(\chi_{2368}(1031,\cdot)\) \(\chi_{2368}(1223,\cdot)\) \(\chi_{2368}(1271,\cdot)\) \(\chi_{2368}(1319,\cdot)\) \(\chi_{2368}(1367,\cdot)\) \(\chi_{2368}(1559,\cdot)\) \(\chi_{2368}(1687,\cdot)\) \(\chi_{2368}(1719,\cdot)\) \(\chi_{2368}(1831,\cdot)\) \(\chi_{2368}(1943,\cdot)\) \(\chi_{2368}(2055,\cdot)\) \(\chi_{2368}(2087,\cdot)\) \(\chi_{2368}(2215,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((1407,1925,705)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{1}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2368 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{17}{72}\right)\) |