Basic properties
Modulus: | \(1792\) | |
Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | 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 1792.ca
\(\chi_{1792}(5,\cdot)\) \(\chi_{1792}(45,\cdot)\) \(\chi_{1792}(61,\cdot)\) \(\chi_{1792}(101,\cdot)\) \(\chi_{1792}(117,\cdot)\) \(\chi_{1792}(157,\cdot)\) \(\chi_{1792}(173,\cdot)\) \(\chi_{1792}(213,\cdot)\) \(\chi_{1792}(229,\cdot)\) \(\chi_{1792}(269,\cdot)\) \(\chi_{1792}(285,\cdot)\) \(\chi_{1792}(325,\cdot)\) \(\chi_{1792}(341,\cdot)\) \(\chi_{1792}(381,\cdot)\) \(\chi_{1792}(397,\cdot)\) \(\chi_{1792}(437,\cdot)\) \(\chi_{1792}(453,\cdot)\) \(\chi_{1792}(493,\cdot)\) \(\chi_{1792}(509,\cdot)\) \(\chi_{1792}(549,\cdot)\) \(\chi_{1792}(565,\cdot)\) \(\chi_{1792}(605,\cdot)\) \(\chi_{1792}(621,\cdot)\) \(\chi_{1792}(661,\cdot)\) \(\chi_{1792}(677,\cdot)\) \(\chi_{1792}(717,\cdot)\) \(\chi_{1792}(733,\cdot)\) \(\chi_{1792}(773,\cdot)\) \(\chi_{1792}(789,\cdot)\) \(\chi_{1792}(829,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{41}{64}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(229, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{192}\right)\) | \(e\left(\frac{155}{192}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{151}{192}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{173}{192}\right)\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{59}{96}\right)\) |