Basic properties
Modulus: | \(2500\) | |
Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{625}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2500.w
\(\chi_{2500}(13,\cdot)\) \(\chi_{2500}(17,\cdot)\) \(\chi_{2500}(33,\cdot)\) \(\chi_{2500}(37,\cdot)\) \(\chi_{2500}(53,\cdot)\) \(\chi_{2500}(73,\cdot)\) \(\chi_{2500}(77,\cdot)\) \(\chi_{2500}(97,\cdot)\) \(\chi_{2500}(113,\cdot)\) \(\chi_{2500}(117,\cdot)\) \(\chi_{2500}(133,\cdot)\) \(\chi_{2500}(137,\cdot)\) \(\chi_{2500}(153,\cdot)\) \(\chi_{2500}(173,\cdot)\) \(\chi_{2500}(177,\cdot)\) \(\chi_{2500}(197,\cdot)\) \(\chi_{2500}(213,\cdot)\) \(\chi_{2500}(217,\cdot)\) \(\chi_{2500}(233,\cdot)\) \(\chi_{2500}(237,\cdot)\) \(\chi_{2500}(253,\cdot)\) \(\chi_{2500}(273,\cdot)\) \(\chi_{2500}(277,\cdot)\) \(\chi_{2500}(297,\cdot)\) \(\chi_{2500}(313,\cdot)\) \(\chi_{2500}(317,\cdot)\) \(\chi_{2500}(333,\cdot)\) \(\chi_{2500}(337,\cdot)\) \(\chi_{2500}(353,\cdot)\) \(\chi_{2500}(373,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{500})$ |
Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((1251,1877)\) → \((1,e\left(\frac{83}{500}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 2500 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{381}{500}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{131}{250}\right)\) | \(e\left(\frac{2}{125}\right)\) | \(e\left(\frac{37}{500}\right)\) | \(e\left(\frac{359}{500}\right)\) | \(e\left(\frac{97}{250}\right)\) | \(e\left(\frac{34}{125}\right)\) | \(e\left(\frac{273}{500}\right)\) | \(e\left(\frac{143}{500}\right)\) |