Basic properties
Modulus: | \(3234\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{539}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.ce
\(\chi_{3234}(25,\cdot)\) \(\chi_{3234}(37,\cdot)\) \(\chi_{3234}(163,\cdot)\) \(\chi_{3234}(235,\cdot)\) \(\chi_{3234}(247,\cdot)\) \(\chi_{3234}(289,\cdot)\) \(\chi_{3234}(445,\cdot)\) \(\chi_{3234}(487,\cdot)\) \(\chi_{3234}(499,\cdot)\) \(\chi_{3234}(625,\cdot)\) \(\chi_{3234}(697,\cdot)\) \(\chi_{3234}(709,\cdot)\) \(\chi_{3234}(751,\cdot)\) \(\chi_{3234}(823,\cdot)\) \(\chi_{3234}(907,\cdot)\) \(\chi_{3234}(1087,\cdot)\) \(\chi_{3234}(1159,\cdot)\) \(\chi_{3234}(1171,\cdot)\) \(\chi_{3234}(1213,\cdot)\) \(\chi_{3234}(1285,\cdot)\) \(\chi_{3234}(1369,\cdot)\) \(\chi_{3234}(1411,\cdot)\) \(\chi_{3234}(1423,\cdot)\) \(\chi_{3234}(1621,\cdot)\) \(\chi_{3234}(1633,\cdot)\) \(\chi_{3234}(1675,\cdot)\) \(\chi_{3234}(1747,\cdot)\) \(\chi_{3234}(1873,\cdot)\) \(\chi_{3234}(1885,\cdot)\) \(\chi_{3234}(2011,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((1079,199,2059)\) → \((1,e\left(\frac{10}{21}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(1633, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{12}{35}\right)\) |