Basic properties
Modulus: | \(2304\) | |
Conductor: | \(2304\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.cd
\(\chi_{2304}(11,\cdot)\) \(\chi_{2304}(59,\cdot)\) \(\chi_{2304}(83,\cdot)\) \(\chi_{2304}(131,\cdot)\) \(\chi_{2304}(155,\cdot)\) \(\chi_{2304}(203,\cdot)\) \(\chi_{2304}(227,\cdot)\) \(\chi_{2304}(275,\cdot)\) \(\chi_{2304}(299,\cdot)\) \(\chi_{2304}(347,\cdot)\) \(\chi_{2304}(371,\cdot)\) \(\chi_{2304}(419,\cdot)\) \(\chi_{2304}(443,\cdot)\) \(\chi_{2304}(491,\cdot)\) \(\chi_{2304}(515,\cdot)\) \(\chi_{2304}(563,\cdot)\) \(\chi_{2304}(587,\cdot)\) \(\chi_{2304}(635,\cdot)\) \(\chi_{2304}(659,\cdot)\) \(\chi_{2304}(707,\cdot)\) \(\chi_{2304}(731,\cdot)\) \(\chi_{2304}(779,\cdot)\) \(\chi_{2304}(803,\cdot)\) \(\chi_{2304}(851,\cdot)\) \(\chi_{2304}(875,\cdot)\) \(\chi_{2304}(923,\cdot)\) \(\chi_{2304}(947,\cdot)\) \(\chi_{2304}(995,\cdot)\) \(\chi_{2304}(1019,\cdot)\) \(\chi_{2304}(1067,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1279,2053,1793)\) → \((-1,e\left(\frac{63}{64}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2304 }(563, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{192}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{1}{192}\right)\) | \(e\left(\frac{179}{192}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{175}{192}\right)\) | \(e\left(\frac{1}{24}\right)\) |