Basic properties
| Modulus: | \(3997\) | |
| Conductor: | \(571\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{571}(22,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3997.ck
\(\chi_{3997}(15,\cdot)\) \(\chi_{3997}(22,\cdot)\) \(\chi_{3997}(50,\cdot)\) \(\chi_{3997}(162,\cdot)\) \(\chi_{3997}(288,\cdot)\) \(\chi_{3997}(365,\cdot)\) \(\chi_{3997}(533,\cdot)\) \(\chi_{3997}(666,\cdot)\) \(\chi_{3997}(806,\cdot)\) \(\chi_{3997}(848,\cdot)\) \(\chi_{3997}(953,\cdot)\) \(\chi_{3997}(960,\cdot)\) \(\chi_{3997}(988,\cdot)\) \(\chi_{3997}(1037,\cdot)\) \(\chi_{3997}(1086,\cdot)\) \(\chi_{3997}(1093,\cdot)\) \(\chi_{3997}(1149,\cdot)\) \(\chi_{3997}(1184,\cdot)\) \(\chi_{3997}(1282,\cdot)\) \(\chi_{3997}(1303,\cdot)\) \(\chi_{3997}(1359,\cdot)\) \(\chi_{3997}(1394,\cdot)\) \(\chi_{3997}(1408,\cdot)\) \(\chi_{3997}(1485,\cdot)\) \(\chi_{3997}(1527,\cdot)\) \(\chi_{3997}(1534,\cdot)\) \(\chi_{3997}(1555,\cdot)\) \(\chi_{3997}(1590,\cdot)\) \(\chi_{3997}(1800,\cdot)\) \(\chi_{3997}(1835,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((1,e\left(\frac{81}{190}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3997 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{81}{190}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{73}{95}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{81}{95}\right)\) | \(e\left(\frac{47}{190}\right)\) | \(e\left(\frac{24}{95}\right)\) | \(e\left(\frac{21}{190}\right)\) |