Basic properties
Modulus: | \(1143\) | |
Conductor: | \(127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{127}(82,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1143.ca
\(\chi_{1143}(82,\cdot)\) \(\chi_{1143}(136,\cdot)\) \(\chi_{1143}(145,\cdot)\) \(\chi_{1143}(163,\cdot)\) \(\chi_{1143}(199,\cdot)\) \(\chi_{1143}(208,\cdot)\) \(\chi_{1143}(271,\cdot)\) \(\chi_{1143}(280,\cdot)\) \(\chi_{1143}(289,\cdot)\) \(\chi_{1143}(298,\cdot)\) \(\chi_{1143}(316,\cdot)\) \(\chi_{1143}(325,\cdot)\) \(\chi_{1143}(352,\cdot)\) \(\chi_{1143}(415,\cdot)\) \(\chi_{1143}(451,\cdot)\) \(\chi_{1143}(460,\cdot)\) \(\chi_{1143}(469,\cdot)\) \(\chi_{1143}(496,\cdot)\) \(\chi_{1143}(505,\cdot)\) \(\chi_{1143}(523,\cdot)\) \(\chi_{1143}(550,\cdot)\) \(\chi_{1143}(568,\cdot)\) \(\chi_{1143}(577,\cdot)\) \(\chi_{1143}(676,\cdot)\) \(\chi_{1143}(739,\cdot)\) \(\chi_{1143}(748,\cdot)\) \(\chi_{1143}(775,\cdot)\) \(\chi_{1143}(793,\cdot)\) \(\chi_{1143}(811,\cdot)\) \(\chi_{1143}(883,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((128,892)\) → \((1,e\left(\frac{13}{63}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 1143 }(82, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{3}{7}\right)\) |