Basic properties
| Modulus: | \(9036\) | |
| Conductor: | \(2259\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2259}(497,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9036.bs
\(\chi_{9036}(497,\cdot)\) \(\chi_{9036}(653,\cdot)\) \(\chi_{9036}(689,\cdot)\) \(\chi_{9036}(749,\cdot)\) \(\chi_{9036}(761,\cdot)\) \(\chi_{9036}(941,\cdot)\) \(\chi_{9036}(1265,\cdot)\) \(\chi_{9036}(1481,\cdot)\) \(\chi_{9036}(1553,\cdot)\) \(\chi_{9036}(2165,\cdot)\) \(\chi_{9036}(2261,\cdot)\) \(\chi_{9036}(2309,\cdot)\) \(\chi_{9036}(2441,\cdot)\) \(\chi_{9036}(2801,\cdot)\) \(\chi_{9036}(2921,\cdot)\) \(\chi_{9036}(3389,\cdot)\) \(\chi_{9036}(3665,\cdot)\) \(\chi_{9036}(3701,\cdot)\) \(\chi_{9036}(3749,\cdot)\) \(\chi_{9036}(3773,\cdot)\) \(\chi_{9036}(3893,\cdot)\) \(\chi_{9036}(3953,\cdot)\) \(\chi_{9036}(3965,\cdot)\) \(\chi_{9036}(4277,\cdot)\) \(\chi_{9036}(4493,\cdot)\) \(\chi_{9036}(4565,\cdot)\) \(\chi_{9036}(5177,\cdot)\) \(\chi_{9036}(5321,\cdot)\) \(\chi_{9036}(5693,\cdot)\) \(\chi_{9036}(5933,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((4519,2009,1261)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{1}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9036 }(497, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{29}{75}\right)\) | \(e\left(\frac{73}{75}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{47}{150}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{62}{75}\right)\) | \(e\left(\frac{4}{75}\right)\) |