Basic properties
| Modulus: | \(8100\) | |
| Conductor: | \(8100\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(270\) | 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 8100.dn
\(\chi_{8100}(59,\cdot)\) \(\chi_{8100}(119,\cdot)\) \(\chi_{8100}(239,\cdot)\) \(\chi_{8100}(419,\cdot)\) \(\chi_{8100}(479,\cdot)\) \(\chi_{8100}(659,\cdot)\) \(\chi_{8100}(779,\cdot)\) \(\chi_{8100}(839,\cdot)\) \(\chi_{8100}(959,\cdot)\) \(\chi_{8100}(1019,\cdot)\) \(\chi_{8100}(1139,\cdot)\) \(\chi_{8100}(1319,\cdot)\) \(\chi_{8100}(1379,\cdot)\) \(\chi_{8100}(1559,\cdot)\) \(\chi_{8100}(1679,\cdot)\) \(\chi_{8100}(1739,\cdot)\) \(\chi_{8100}(1859,\cdot)\) \(\chi_{8100}(1919,\cdot)\) \(\chi_{8100}(2039,\cdot)\) \(\chi_{8100}(2219,\cdot)\) \(\chi_{8100}(2279,\cdot)\) \(\chi_{8100}(2459,\cdot)\) \(\chi_{8100}(2579,\cdot)\) \(\chi_{8100}(2639,\cdot)\) \(\chi_{8100}(2759,\cdot)\) \(\chi_{8100}(2819,\cdot)\) \(\chi_{8100}(2939,\cdot)\) \(\chi_{8100}(3119,\cdot)\) \(\chi_{8100}(3179,\cdot)\) \(\chi_{8100}(3359,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{135})$ |
| Fixed field: | Number field defined by a degree 270 polynomial (not computed) |
Values on generators
\((4051,6401,7777)\) → \((-1,e\left(\frac{41}{54}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8100 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{77}{135}\right)\) | \(e\left(\frac{101}{270}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{149}{270}\right)\) | \(e\left(\frac{133}{270}\right)\) | \(e\left(\frac{77}{270}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{11}{270}\right)\) |