Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(6270\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{43681}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.dl
\(\chi_{87362}(7,\cdot)\) \(\chi_{87362}(83,\cdot)\) \(\chi_{87362}(277,\cdot)\) \(\chi_{87362}(315,\cdot)\) \(\chi_{87362}(349,\cdot)\) \(\chi_{87362}(387,\cdot)\) \(\chi_{87362}(391,\cdot)\) \(\chi_{87362}(425,\cdot)\) \(\chi_{87362}(501,\cdot)\) \(\chi_{87362}(657,\cdot)\) \(\chi_{87362}(695,\cdot)\) \(\chi_{87362}(733,\cdot)\) \(\chi_{87362}(767,\cdot)\) \(\chi_{87362}(805,\cdot)\) \(\chi_{87362}(809,\cdot)\) \(\chi_{87362}(843,\cdot)\) \(\chi_{87362}(919,\cdot)\) \(\chi_{87362}(1075,\cdot)\) \(\chi_{87362}(1113,\cdot)\) \(\chi_{87362}(1185,\cdot)\) \(\chi_{87362}(1223,\cdot)\) \(\chi_{87362}(1227,\cdot)\) \(\chi_{87362}(1261,\cdot)\) \(\chi_{87362}(1337,\cdot)\) \(\chi_{87362}(1493,\cdot)\) \(\chi_{87362}(1531,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{3135})$ |
| Fixed field: | Number field defined by a degree 6270 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{7}{110}\right),e\left(\frac{25}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{161}{285}\right)\) | \(e\left(\frac{1453}{3135}\right)\) | \(e\left(\frac{491}{2090}\right)\) | \(e\left(\frac{37}{285}\right)\) | \(e\left(\frac{4549}{6270}\right)\) | \(e\left(\frac{89}{3135}\right)\) | \(e\left(\frac{1511}{6270}\right)\) | \(e\left(\frac{1003}{1254}\right)\) | \(e\left(\frac{307}{627}\right)\) | \(e\left(\frac{2906}{3135}\right)\) |