Basic properties
| Modulus: | \(7448\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(842,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7448.ic
\(\chi_{7448}(9,\cdot)\) \(\chi_{7448}(81,\cdot)\) \(\chi_{7448}(289,\cdot)\) \(\chi_{7448}(473,\cdot)\) \(\chi_{7448}(529,\cdot)\) \(\chi_{7448}(1073,\cdot)\) \(\chi_{7448}(1241,\cdot)\) \(\chi_{7448}(1593,\cdot)\) \(\chi_{7448}(2209,\cdot)\) \(\chi_{7448}(2305,\cdot)\) \(\chi_{7448}(2417,\cdot)\) \(\chi_{7448}(2601,\cdot)\) \(\chi_{7448}(2657,\cdot)\) \(\chi_{7448}(3201,\cdot)\) \(\chi_{7448}(3273,\cdot)\) \(\chi_{7448}(3369,\cdot)\) \(\chi_{7448}(3481,\cdot)\) \(\chi_{7448}(3665,\cdot)\) \(\chi_{7448}(3721,\cdot)\) \(\chi_{7448}(4265,\cdot)\) \(\chi_{7448}(4337,\cdot)\) \(\chi_{7448}(4433,\cdot)\) \(\chi_{7448}(4545,\cdot)\) \(\chi_{7448}(4729,\cdot)\) \(\chi_{7448}(4785,\cdot)\) \(\chi_{7448}(5329,\cdot)\) \(\chi_{7448}(5401,\cdot)\) \(\chi_{7448}(5497,\cdot)\) \(\chi_{7448}(5609,\cdot)\) \(\chi_{7448}(5793,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((1863,3725,3041,3137)\) → \((1,1,e\left(\frac{1}{21}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 7448 }(5497, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) |