Basic properties
Modulus: | \(2304\) | |
Conductor: | \(2304\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.ca
\(\chi_{2304}(13,\cdot)\) \(\chi_{2304}(61,\cdot)\) \(\chi_{2304}(85,\cdot)\) \(\chi_{2304}(133,\cdot)\) \(\chi_{2304}(157,\cdot)\) \(\chi_{2304}(205,\cdot)\) \(\chi_{2304}(229,\cdot)\) \(\chi_{2304}(277,\cdot)\) \(\chi_{2304}(301,\cdot)\) \(\chi_{2304}(349,\cdot)\) \(\chi_{2304}(373,\cdot)\) \(\chi_{2304}(421,\cdot)\) \(\chi_{2304}(445,\cdot)\) \(\chi_{2304}(493,\cdot)\) \(\chi_{2304}(517,\cdot)\) \(\chi_{2304}(565,\cdot)\) \(\chi_{2304}(589,\cdot)\) \(\chi_{2304}(637,\cdot)\) \(\chi_{2304}(661,\cdot)\) \(\chi_{2304}(709,\cdot)\) \(\chi_{2304}(733,\cdot)\) \(\chi_{2304}(781,\cdot)\) \(\chi_{2304}(805,\cdot)\) \(\chi_{2304}(853,\cdot)\) \(\chi_{2304}(877,\cdot)\) \(\chi_{2304}(925,\cdot)\) \(\chi_{2304}(949,\cdot)\) \(\chi_{2304}(997,\cdot)\) \(\chi_{2304}(1021,\cdot)\) \(\chi_{2304}(1069,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1279,2053,1793)\) → \((1,e\left(\frac{11}{64}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2304 }(733, a) \) | \(1\) | \(1\) | \(e\left(\frac{161}{192}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{181}{192}\right)\) | \(e\left(\frac{143}{192}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{91}{192}\right)\) | \(e\left(\frac{1}{24}\right)\) |