Basic properties
| Modulus: | \(5625\) | |
| Conductor: | \(1875\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1875}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5625.bq
\(\chi_{5625}(8,\cdot)\) \(\chi_{5625}(17,\cdot)\) \(\chi_{5625}(53,\cdot)\) \(\chi_{5625}(62,\cdot)\) \(\chi_{5625}(98,\cdot)\) \(\chi_{5625}(152,\cdot)\) \(\chi_{5625}(188,\cdot)\) \(\chi_{5625}(197,\cdot)\) \(\chi_{5625}(233,\cdot)\) \(\chi_{5625}(242,\cdot)\) \(\chi_{5625}(278,\cdot)\) \(\chi_{5625}(287,\cdot)\) \(\chi_{5625}(323,\cdot)\) \(\chi_{5625}(377,\cdot)\) \(\chi_{5625}(413,\cdot)\) \(\chi_{5625}(422,\cdot)\) \(\chi_{5625}(458,\cdot)\) \(\chi_{5625}(467,\cdot)\) \(\chi_{5625}(503,\cdot)\) \(\chi_{5625}(512,\cdot)\) \(\chi_{5625}(548,\cdot)\) \(\chi_{5625}(602,\cdot)\) \(\chi_{5625}(638,\cdot)\) \(\chi_{5625}(647,\cdot)\) \(\chi_{5625}(683,\cdot)\) \(\chi_{5625}(692,\cdot)\) \(\chi_{5625}(728,\cdot)\) \(\chi_{5625}(737,\cdot)\) \(\chi_{5625}(773,\cdot)\) \(\chi_{5625}(827,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((4376,1252)\) → \((-1,e\left(\frac{3}{500}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5625 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{253}{500}\right)\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{259}{500}\right)\) | \(e\left(\frac{89}{250}\right)\) | \(e\left(\frac{417}{500}\right)\) | \(e\left(\frac{52}{125}\right)\) | \(e\left(\frac{3}{125}\right)\) | \(e\left(\frac{269}{500}\right)\) | \(e\left(\frac{127}{250}\right)\) |