Basic properties
Modulus: | \(6422\) | |
Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3211}(1047,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6422.dn
\(\chi_{6422}(15,\cdot)\) \(\chi_{6422}(33,\cdot)\) \(\chi_{6422}(59,\cdot)\) \(\chi_{6422}(67,\cdot)\) \(\chi_{6422}(71,\cdot)\) \(\chi_{6422}(97,\cdot)\) \(\chi_{6422}(167,\cdot)\) \(\chi_{6422}(219,\cdot)\) \(\chi_{6422}(345,\cdot)\) \(\chi_{6422}(383,\cdot)\) \(\chi_{6422}(431,\cdot)\) \(\chi_{6422}(509,\cdot)\) \(\chi_{6422}(527,\cdot)\) \(\chi_{6422}(553,\cdot)\) \(\chi_{6422}(561,\cdot)\) \(\chi_{6422}(565,\cdot)\) \(\chi_{6422}(583,\cdot)\) \(\chi_{6422}(591,\cdot)\) \(\chi_{6422}(661,\cdot)\) \(\chi_{6422}(713,\cdot)\) \(\chi_{6422}(839,\cdot)\) \(\chi_{6422}(877,\cdot)\) \(\chi_{6422}(1003,\cdot)\) \(\chi_{6422}(1021,\cdot)\) \(\chi_{6422}(1047,\cdot)\) \(\chi_{6422}(1055,\cdot)\) \(\chi_{6422}(1059,\cdot)\) \(\chi_{6422}(1077,\cdot)\) \(\chi_{6422}(1085,\cdot)\) \(\chi_{6422}(1155,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((4903,4733)\) → \((e\left(\frac{71}{156}\right),e\left(\frac{1}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 6422 }(1047, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{37}{117}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{67}{468}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{227}{234}\right)\) |