Basic properties
Modulus: | \(8670\) | |
Conductor: | \(1445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1445}(37,\cdot)\) | 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 8670.cn
\(\chi_{8670}(37,\cdot)\) \(\chi_{8670}(97,\cdot)\) \(\chi_{8670}(163,\cdot)\) \(\chi_{8670}(193,\cdot)\) \(\chi_{8670}(277,\cdot)\) \(\chi_{8670}(283,\cdot)\) \(\chi_{8670}(313,\cdot)\) \(\chi_{8670}(337,\cdot)\) \(\chi_{8670}(547,\cdot)\) \(\chi_{8670}(607,\cdot)\) \(\chi_{8670}(673,\cdot)\) \(\chi_{8670}(703,\cdot)\) \(\chi_{8670}(787,\cdot)\) \(\chi_{8670}(793,\cdot)\) \(\chi_{8670}(823,\cdot)\) \(\chi_{8670}(847,\cdot)\) \(\chi_{8670}(1057,\cdot)\) \(\chi_{8670}(1117,\cdot)\) \(\chi_{8670}(1183,\cdot)\) \(\chi_{8670}(1213,\cdot)\) \(\chi_{8670}(1297,\cdot)\) \(\chi_{8670}(1303,\cdot)\) \(\chi_{8670}(1333,\cdot)\) \(\chi_{8670}(1357,\cdot)\) \(\chi_{8670}(1567,\cdot)\) \(\chi_{8670}(1627,\cdot)\) \(\chi_{8670}(1693,\cdot)\) \(\chi_{8670}(1723,\cdot)\) \(\chi_{8670}(1807,\cdot)\) \(\chi_{8670}(1813,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{272})$ |
Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2891,6937,6361)\) → \((1,i,e\left(\frac{129}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8670 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{207}{272}\right)\) | \(e\left(\frac{247}{272}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{139}{272}\right)\) | \(e\left(\frac{213}{272}\right)\) | \(e\left(\frac{73}{272}\right)\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{27}{272}\right)\) | \(e\left(\frac{127}{136}\right)\) |