Basic properties
Modulus: | \(2592\) | |
Conductor: | \(1296\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1296}(997,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2592.ch
\(\chi_{2592}(25,\cdot)\) \(\chi_{2592}(121,\cdot)\) \(\chi_{2592}(169,\cdot)\) \(\chi_{2592}(265,\cdot)\) \(\chi_{2592}(313,\cdot)\) \(\chi_{2592}(409,\cdot)\) \(\chi_{2592}(457,\cdot)\) \(\chi_{2592}(553,\cdot)\) \(\chi_{2592}(601,\cdot)\) \(\chi_{2592}(697,\cdot)\) \(\chi_{2592}(745,\cdot)\) \(\chi_{2592}(841,\cdot)\) \(\chi_{2592}(889,\cdot)\) \(\chi_{2592}(985,\cdot)\) \(\chi_{2592}(1033,\cdot)\) \(\chi_{2592}(1129,\cdot)\) \(\chi_{2592}(1177,\cdot)\) \(\chi_{2592}(1273,\cdot)\) \(\chi_{2592}(1321,\cdot)\) \(\chi_{2592}(1417,\cdot)\) \(\chi_{2592}(1465,\cdot)\) \(\chi_{2592}(1561,\cdot)\) \(\chi_{2592}(1609,\cdot)\) \(\chi_{2592}(1705,\cdot)\) \(\chi_{2592}(1753,\cdot)\) \(\chi_{2592}(1849,\cdot)\) \(\chi_{2592}(1897,\cdot)\) \(\chi_{2592}(1993,\cdot)\) \(\chi_{2592}(2041,\cdot)\) \(\chi_{2592}(2137,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((1,i,e\left(\frac{23}{27}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2592 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{1}{27}\right)\) |