Basic properties
| Modulus: | \(1045\) | |
| Conductor: | \(1045\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 1045.cr
\(\chi_{1045}(3,\cdot)\) \(\chi_{1045}(48,\cdot)\) \(\chi_{1045}(53,\cdot)\) \(\chi_{1045}(97,\cdot)\) \(\chi_{1045}(108,\cdot)\) \(\chi_{1045}(147,\cdot)\) \(\chi_{1045}(148,\cdot)\) \(\chi_{1045}(192,\cdot)\) \(\chi_{1045}(203,\cdot)\) \(\chi_{1045}(212,\cdot)\) \(\chi_{1045}(223,\cdot)\) \(\chi_{1045}(257,\cdot)\) \(\chi_{1045}(262,\cdot)\) \(\chi_{1045}(268,\cdot)\) \(\chi_{1045}(317,\cdot)\) \(\chi_{1045}(333,\cdot)\) \(\chi_{1045}(357,\cdot)\) \(\chi_{1045}(383,\cdot)\) \(\chi_{1045}(412,\cdot)\) \(\chi_{1045}(432,\cdot)\) \(\chi_{1045}(433,\cdot)\) \(\chi_{1045}(477,\cdot)\) \(\chi_{1045}(478,\cdot)\) \(\chi_{1045}(488,\cdot)\) \(\chi_{1045}(542,\cdot)\) \(\chi_{1045}(553,\cdot)\) \(\chi_{1045}(592,\cdot)\) \(\chi_{1045}(603,\cdot)\) \(\chi_{1045}(642,\cdot)\) \(\chi_{1045}(687,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((837,761,496)\) → \((i,e\left(\frac{4}{5}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(432, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{28}{45}\right)\) |