Basic properties
| Modulus: | \(3240\) | |
| Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{405}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3240.do
\(\chi_{3240}(113,\cdot)\) \(\chi_{3240}(137,\cdot)\) \(\chi_{3240}(257,\cdot)\) \(\chi_{3240}(353,\cdot)\) \(\chi_{3240}(473,\cdot)\) \(\chi_{3240}(497,\cdot)\) \(\chi_{3240}(617,\cdot)\) \(\chi_{3240}(713,\cdot)\) \(\chi_{3240}(833,\cdot)\) \(\chi_{3240}(857,\cdot)\) \(\chi_{3240}(977,\cdot)\) \(\chi_{3240}(1073,\cdot)\) \(\chi_{3240}(1193,\cdot)\) \(\chi_{3240}(1217,\cdot)\) \(\chi_{3240}(1337,\cdot)\) \(\chi_{3240}(1433,\cdot)\) \(\chi_{3240}(1553,\cdot)\) \(\chi_{3240}(1577,\cdot)\) \(\chi_{3240}(1697,\cdot)\) \(\chi_{3240}(1793,\cdot)\) \(\chi_{3240}(1913,\cdot)\) \(\chi_{3240}(1937,\cdot)\) \(\chi_{3240}(2057,\cdot)\) \(\chi_{3240}(2153,\cdot)\) \(\chi_{3240}(2273,\cdot)\) \(\chi_{3240}(2297,\cdot)\) \(\chi_{3240}(2417,\cdot)\) \(\chi_{3240}(2513,\cdot)\) \(\chi_{3240}(2633,\cdot)\) \(\chi_{3240}(2657,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,3161,1297)\) → \((1,1,e\left(\frac{5}{54}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3240 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{108}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{49}{54}\right)\) |