Basic properties
Modulus: | \(6422\) | |
Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3211}(789,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 6422.dd
\(\chi_{6422}(3,\cdot)\) \(\chi_{6422}(165,\cdot)\) \(\chi_{6422}(185,\cdot)\) \(\chi_{6422}(211,\cdot)\) \(\chi_{6422}(243,\cdot)\) \(\chi_{6422}(295,\cdot)\) \(\chi_{6422}(497,\cdot)\) \(\chi_{6422}(659,\cdot)\) \(\chi_{6422}(679,\cdot)\) \(\chi_{6422}(705,\cdot)\) \(\chi_{6422}(737,\cdot)\) \(\chi_{6422}(789,\cdot)\) \(\chi_{6422}(1153,\cdot)\) \(\chi_{6422}(1173,\cdot)\) \(\chi_{6422}(1199,\cdot)\) \(\chi_{6422}(1231,\cdot)\) \(\chi_{6422}(1283,\cdot)\) \(\chi_{6422}(1485,\cdot)\) \(\chi_{6422}(1647,\cdot)\) \(\chi_{6422}(1693,\cdot)\) \(\chi_{6422}(1725,\cdot)\) \(\chi_{6422}(1777,\cdot)\) \(\chi_{6422}(1979,\cdot)\) \(\chi_{6422}(2141,\cdot)\) \(\chi_{6422}(2161,\cdot)\) \(\chi_{6422}(2187,\cdot)\) \(\chi_{6422}(2271,\cdot)\) \(\chi_{6422}(2473,\cdot)\) \(\chi_{6422}(2635,\cdot)\) \(\chi_{6422}(2655,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{8}{39}\right),e\left(\frac{17}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 6422 }(789, a) \) | \(-1\) | \(1\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{112}{117}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{77}{234}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{107}{117}\right)\) |