Basic properties
| Modulus: | \(1815\) | |
| Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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 1815.bu
\(\chi_{1815}(38,\cdot)\) \(\chi_{1815}(47,\cdot)\) \(\chi_{1815}(53,\cdot)\) \(\chi_{1815}(92,\cdot)\) \(\chi_{1815}(113,\cdot)\) \(\chi_{1815}(137,\cdot)\) \(\chi_{1815}(152,\cdot)\) \(\chi_{1815}(158,\cdot)\) \(\chi_{1815}(203,\cdot)\) \(\chi_{1815}(212,\cdot)\) \(\chi_{1815}(218,\cdot)\) \(\chi_{1815}(257,\cdot)\) \(\chi_{1815}(278,\cdot)\) \(\chi_{1815}(302,\cdot)\) \(\chi_{1815}(317,\cdot)\) \(\chi_{1815}(368,\cdot)\) \(\chi_{1815}(377,\cdot)\) \(\chi_{1815}(383,\cdot)\) \(\chi_{1815}(422,\cdot)\) \(\chi_{1815}(443,\cdot)\) \(\chi_{1815}(467,\cdot)\) \(\chi_{1815}(482,\cdot)\) \(\chi_{1815}(488,\cdot)\) \(\chi_{1815}(533,\cdot)\) \(\chi_{1815}(542,\cdot)\) \(\chi_{1815}(548,\cdot)\) \(\chi_{1815}(587,\cdot)\) \(\chi_{1815}(647,\cdot)\) \(\chi_{1815}(653,\cdot)\) \(\chi_{1815}(698,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((-1,i,e\left(\frac{28}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1815 }(482, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{220}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{171}{220}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{39}{44}\right)\) |