Basic properties
| Modulus: | \(3240\) | |
| Conductor: | \(3240\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3240.dk
\(\chi_{3240}(77,\cdot)\) \(\chi_{3240}(173,\cdot)\) \(\chi_{3240}(293,\cdot)\) \(\chi_{3240}(317,\cdot)\) \(\chi_{3240}(437,\cdot)\) \(\chi_{3240}(533,\cdot)\) \(\chi_{3240}(653,\cdot)\) \(\chi_{3240}(677,\cdot)\) \(\chi_{3240}(797,\cdot)\) \(\chi_{3240}(893,\cdot)\) \(\chi_{3240}(1013,\cdot)\) \(\chi_{3240}(1037,\cdot)\) \(\chi_{3240}(1157,\cdot)\) \(\chi_{3240}(1253,\cdot)\) \(\chi_{3240}(1373,\cdot)\) \(\chi_{3240}(1397,\cdot)\) \(\chi_{3240}(1517,\cdot)\) \(\chi_{3240}(1613,\cdot)\) \(\chi_{3240}(1733,\cdot)\) \(\chi_{3240}(1757,\cdot)\) \(\chi_{3240}(1877,\cdot)\) \(\chi_{3240}(1973,\cdot)\) \(\chi_{3240}(2093,\cdot)\) \(\chi_{3240}(2117,\cdot)\) \(\chi_{3240}(2237,\cdot)\) \(\chi_{3240}(2333,\cdot)\) \(\chi_{3240}(2453,\cdot)\) \(\chi_{3240}(2477,\cdot)\) \(\chi_{3240}(2597,\cdot)\) \(\chi_{3240}(2693,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,3161,1297)\) → \((1,-1,e\left(\frac{29}{54}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3240 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{59}{108}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{25}{54}\right)\) |