Basic properties
| Modulus: | \(1728\) | |
| 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 \(\chi_{864}(133,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1728.cc
\(\chi_{1728}(25,\cdot)\) \(\chi_{1728}(121,\cdot)\) \(\chi_{1728}(169,\cdot)\) \(\chi_{1728}(265,\cdot)\) \(\chi_{1728}(313,\cdot)\) \(\chi_{1728}(409,\cdot)\) \(\chi_{1728}(457,\cdot)\) \(\chi_{1728}(553,\cdot)\) \(\chi_{1728}(601,\cdot)\) \(\chi_{1728}(697,\cdot)\) \(\chi_{1728}(745,\cdot)\) \(\chi_{1728}(841,\cdot)\) \(\chi_{1728}(889,\cdot)\) \(\chi_{1728}(985,\cdot)\) \(\chi_{1728}(1033,\cdot)\) \(\chi_{1728}(1129,\cdot)\) \(\chi_{1728}(1177,\cdot)\) \(\chi_{1728}(1273,\cdot)\) \(\chi_{1728}(1321,\cdot)\) \(\chi_{1728}(1417,\cdot)\) \(\chi_{1728}(1465,\cdot)\) \(\chi_{1728}(1561,\cdot)\) \(\chi_{1728}(1609,\cdot)\) \(\chi_{1728}(1705,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((703,325,1217)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1728 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) |