Basic properties
| Modulus: | \(9216\) | |
| Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{256}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9216.bt
\(\chi_{9216}(145,\cdot)\) \(\chi_{9216}(433,\cdot)\) \(\chi_{9216}(721,\cdot)\) \(\chi_{9216}(1009,\cdot)\) \(\chi_{9216}(1297,\cdot)\) \(\chi_{9216}(1585,\cdot)\) \(\chi_{9216}(1873,\cdot)\) \(\chi_{9216}(2161,\cdot)\) \(\chi_{9216}(2449,\cdot)\) \(\chi_{9216}(2737,\cdot)\) \(\chi_{9216}(3025,\cdot)\) \(\chi_{9216}(3313,\cdot)\) \(\chi_{9216}(3601,\cdot)\) \(\chi_{9216}(3889,\cdot)\) \(\chi_{9216}(4177,\cdot)\) \(\chi_{9216}(4465,\cdot)\) \(\chi_{9216}(4753,\cdot)\) \(\chi_{9216}(5041,\cdot)\) \(\chi_{9216}(5329,\cdot)\) \(\chi_{9216}(5617,\cdot)\) \(\chi_{9216}(5905,\cdot)\) \(\chi_{9216}(6193,\cdot)\) \(\chi_{9216}(6481,\cdot)\) \(\chi_{9216}(6769,\cdot)\) \(\chi_{9216}(7057,\cdot)\) \(\chi_{9216}(7345,\cdot)\) \(\chi_{9216}(7633,\cdot)\) \(\chi_{9216}(7921,\cdot)\) \(\chi_{9216}(8209,\cdot)\) \(\chi_{9216}(8497,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((8191,2053,4097)\) → \((1,e\left(\frac{31}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9216 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |