Basic properties
Modulus: | \(5241\) | |
Conductor: | \(5241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1746\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5241.w
\(\chi_{5241}(14,\cdot)\) \(\chi_{5241}(17,\cdot)\) \(\chi_{5241}(23,\cdot)\) \(\chi_{5241}(26,\cdot)\) \(\chi_{5241}(29,\cdot)\) \(\chi_{5241}(56,\cdot)\) \(\chi_{5241}(68,\cdot)\) \(\chi_{5241}(74,\cdot)\) \(\chi_{5241}(77,\cdot)\) \(\chi_{5241}(104,\cdot)\) \(\chi_{5241}(113,\cdot)\) \(\chi_{5241}(137,\cdot)\) \(\chi_{5241}(140,\cdot)\) \(\chi_{5241}(143,\cdot)\) \(\chi_{5241}(146,\cdot)\) \(\chi_{5241}(158,\cdot)\) \(\chi_{5241}(164,\cdot)\) \(\chi_{5241}(170,\cdot)\) \(\chi_{5241}(179,\cdot)\) \(\chi_{5241}(191,\cdot)\) \(\chi_{5241}(197,\cdot)\) \(\chi_{5241}(230,\cdot)\) \(\chi_{5241}(233,\cdot)\) \(\chi_{5241}(239,\cdot)\) \(\chi_{5241}(257,\cdot)\) \(\chi_{5241}(260,\cdot)\) \(\chi_{5241}(266,\cdot)\) \(\chi_{5241}(269,\cdot)\) \(\chi_{5241}(290,\cdot)\) \(\chi_{5241}(296,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{873})$ |
Fixed field: | Number field defined by a degree 1746 polynomial (not computed) |
Values on generators
\((1748,3496)\) → \((-1,e\left(\frac{628}{873}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 5241 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{383}{1746}\right)\) | \(e\left(\frac{383}{873}\right)\) | \(e\left(\frac{991}{1746}\right)\) | \(e\left(\frac{736}{873}\right)\) | \(e\left(\frac{383}{582}\right)\) | \(e\left(\frac{229}{291}\right)\) | \(e\left(\frac{367}{582}\right)\) | \(e\left(\frac{694}{873}\right)\) | \(e\left(\frac{109}{1746}\right)\) | \(e\left(\frac{766}{873}\right)\) |