Basic properties
Modulus: | \(3311\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{473}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3311.fd
\(\chi_{3311}(57,\cdot)\) \(\chi_{3311}(239,\cdot)\) \(\chi_{3311}(281,\cdot)\) \(\chi_{3311}(316,\cdot)\) \(\chi_{3311}(358,\cdot)\) \(\chi_{3311}(470,\cdot)\) \(\chi_{3311}(547,\cdot)\) \(\chi_{3311}(568,\cdot)\) \(\chi_{3311}(701,\cdot)\) \(\chi_{3311}(799,\cdot)\) \(\chi_{3311}(827,\cdot)\) \(\chi_{3311}(855,\cdot)\) \(\chi_{3311}(1128,\cdot)\) \(\chi_{3311}(1135,\cdot)\) \(\chi_{3311}(1184,\cdot)\) \(\chi_{3311}(1261,\cdot)\) \(\chi_{3311}(1436,\cdot)\) \(\chi_{3311}(1443,\cdot)\) \(\chi_{3311}(1471,\cdot)\) \(\chi_{3311}(1520,\cdot)\) \(\chi_{3311}(1674,\cdot)\) \(\chi_{3311}(1702,\cdot)\) \(\chi_{3311}(1744,\cdot)\) \(\chi_{3311}(1751,\cdot)\) \(\chi_{3311}(1821,\cdot)\) \(\chi_{3311}(1905,\cdot)\) \(\chi_{3311}(1975,\cdot)\) \(\chi_{3311}(2031,\cdot)\) \(\chi_{3311}(2052,\cdot)\) \(\chi_{3311}(2059,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1893,904,2927)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
\( \chi_{ 3311 }(2031, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{67}{210}\right)\) |