Basic properties
| Modulus: | \(2675\) | |
| Conductor: | \(535\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(212\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{535}(32,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2675.r
\(\chi_{2675}(7,\cdot)\) \(\chi_{2675}(18,\cdot)\) \(\chi_{2675}(32,\cdot)\) \(\chi_{2675}(43,\cdot)\) \(\chi_{2675}(68,\cdot)\) \(\chi_{2675}(82,\cdot)\) \(\chi_{2675}(93,\cdot)\) \(\chi_{2675}(157,\cdot)\) \(\chi_{2675}(232,\cdot)\) \(\chi_{2675}(257,\cdot)\) \(\chi_{2675}(268,\cdot)\) \(\chi_{2675}(282,\cdot)\) \(\chi_{2675}(307,\cdot)\) \(\chi_{2675}(318,\cdot)\) \(\chi_{2675}(343,\cdot)\) \(\chi_{2675}(393,\cdot)\) \(\chi_{2675}(418,\cdot)\) \(\chi_{2675}(443,\cdot)\) \(\chi_{2675}(482,\cdot)\) \(\chi_{2675}(493,\cdot)\) \(\chi_{2675}(532,\cdot)\) \(\chi_{2675}(543,\cdot)\) \(\chi_{2675}(557,\cdot)\) \(\chi_{2675}(593,\cdot)\) \(\chi_{2675}(607,\cdot)\) \(\chi_{2675}(632,\cdot)\) \(\chi_{2675}(657,\cdot)\) \(\chi_{2675}(668,\cdot)\) \(\chi_{2675}(693,\cdot)\) \(\chi_{2675}(707,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{212})$ |
| Fixed field: | Number field defined by a degree 212 polynomial (not computed) |
Values on generators
\((1927,751)\) → \((i,e\left(\frac{5}{106}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2675 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{212}\right)\) | \(e\left(\frac{11}{212}\right)\) | \(e\left(\frac{63}{106}\right)\) | \(e\left(\frac{37}{106}\right)\) | \(e\left(\frac{59}{212}\right)\) | \(e\left(\frac{189}{212}\right)\) | \(e\left(\frac{11}{106}\right)\) | \(e\left(\frac{2}{53}\right)\) | \(e\left(\frac{137}{212}\right)\) | \(e\left(\frac{87}{212}\right)\) |