Basic properties
| Modulus: | \(1075\) | |
| Conductor: | \(1075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | 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 1075.bo
\(\chi_{1075}(31,\cdot)\) \(\chi_{1075}(56,\cdot)\) \(\chi_{1075}(66,\cdot)\) \(\chi_{1075}(81,\cdot)\) \(\chi_{1075}(96,\cdot)\) \(\chi_{1075}(111,\cdot)\) \(\chi_{1075}(146,\cdot)\) \(\chi_{1075}(181,\cdot)\) \(\chi_{1075}(186,\cdot)\) \(\chi_{1075}(196,\cdot)\) \(\chi_{1075}(246,\cdot)\) \(\chi_{1075}(271,\cdot)\) \(\chi_{1075}(281,\cdot)\) \(\chi_{1075}(296,\cdot)\) \(\chi_{1075}(311,\cdot)\) \(\chi_{1075}(316,\cdot)\) \(\chi_{1075}(341,\cdot)\) \(\chi_{1075}(361,\cdot)\) \(\chi_{1075}(396,\cdot)\) \(\chi_{1075}(411,\cdot)\) \(\chi_{1075}(461,\cdot)\) \(\chi_{1075}(486,\cdot)\) \(\chi_{1075}(496,\cdot)\) \(\chi_{1075}(511,\cdot)\) \(\chi_{1075}(531,\cdot)\) \(\chi_{1075}(541,\cdot)\) \(\chi_{1075}(556,\cdot)\) \(\chi_{1075}(611,\cdot)\) \(\chi_{1075}(616,\cdot)\) \(\chi_{1075}(711,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((302,476)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{17}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1075 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) |