Basic properties
| Modulus: | \(9036\) | |
| Conductor: | \(9036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | 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 9036.bw
\(\chi_{9036}(151,\cdot)\) \(\chi_{9036}(187,\cdot)\) \(\chi_{9036}(247,\cdot)\) \(\chi_{9036}(259,\cdot)\) \(\chi_{9036}(439,\cdot)\) \(\chi_{9036}(763,\cdot)\) \(\chi_{9036}(979,\cdot)\) \(\chi_{9036}(1051,\cdot)\) \(\chi_{9036}(1663,\cdot)\) \(\chi_{9036}(1759,\cdot)\) \(\chi_{9036}(1807,\cdot)\) \(\chi_{9036}(1939,\cdot)\) \(\chi_{9036}(2299,\cdot)\) \(\chi_{9036}(2419,\cdot)\) \(\chi_{9036}(2887,\cdot)\) \(\chi_{9036}(3163,\cdot)\) \(\chi_{9036}(3199,\cdot)\) \(\chi_{9036}(3247,\cdot)\) \(\chi_{9036}(3271,\cdot)\) \(\chi_{9036}(3391,\cdot)\) \(\chi_{9036}(3451,\cdot)\) \(\chi_{9036}(3463,\cdot)\) \(\chi_{9036}(3775,\cdot)\) \(\chi_{9036}(3991,\cdot)\) \(\chi_{9036}(4063,\cdot)\) \(\chi_{9036}(4675,\cdot)\) \(\chi_{9036}(4819,\cdot)\) \(\chi_{9036}(5191,\cdot)\) \(\chi_{9036}(5431,\cdot)\) \(\chi_{9036}(5899,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((4519,2009,1261)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{21}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9036 }(151, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{49}{150}\right)\) | \(e\left(\frac{59}{75}\right)\) | \(e\left(\frac{58}{75}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{137}{150}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{79}{150}\right)\) | \(e\left(\frac{143}{150}\right)\) |