Basic properties
| Modulus: | \(2592\) | |
| Conductor: | \(864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{864}(227,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2592.cb
\(\chi_{2592}(35,\cdot)\) \(\chi_{2592}(179,\cdot)\) \(\chi_{2592}(251,\cdot)\) \(\chi_{2592}(395,\cdot)\) \(\chi_{2592}(467,\cdot)\) \(\chi_{2592}(611,\cdot)\) \(\chi_{2592}(683,\cdot)\) \(\chi_{2592}(827,\cdot)\) \(\chi_{2592}(899,\cdot)\) \(\chi_{2592}(1043,\cdot)\) \(\chi_{2592}(1115,\cdot)\) \(\chi_{2592}(1259,\cdot)\) \(\chi_{2592}(1331,\cdot)\) \(\chi_{2592}(1475,\cdot)\) \(\chi_{2592}(1547,\cdot)\) \(\chi_{2592}(1691,\cdot)\) \(\chi_{2592}(1763,\cdot)\) \(\chi_{2592}(1907,\cdot)\) \(\chi_{2592}(1979,\cdot)\) \(\chi_{2592}(2123,\cdot)\) \(\chi_{2592}(2195,\cdot)\) \(\chi_{2592}(2339,\cdot)\) \(\chi_{2592}(2411,\cdot)\) \(\chi_{2592}(2555,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,325,1217)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2592 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) |