Basic properties
| Modulus: | \(3971\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1710\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 3971.bv
\(\chi_{3971}(6,\cdot)\) \(\chi_{3971}(17,\cdot)\) \(\chi_{3971}(24,\cdot)\) \(\chi_{3971}(35,\cdot)\) \(\chi_{3971}(61,\cdot)\) \(\chi_{3971}(63,\cdot)\) \(\chi_{3971}(73,\cdot)\) \(\chi_{3971}(74,\cdot)\) \(\chi_{3971}(85,\cdot)\) \(\chi_{3971}(101,\cdot)\) \(\chi_{3971}(112,\cdot)\) \(\chi_{3971}(118,\cdot)\) \(\chi_{3971}(123,\cdot)\) \(\chi_{3971}(138,\cdot)\) \(\chi_{3971}(139,\cdot)\) \(\chi_{3971}(149,\cdot)\) \(\chi_{3971}(150,\cdot)\) \(\chi_{3971}(156,\cdot)\) \(\chi_{3971}(161,\cdot)\) \(\chi_{3971}(194,\cdot)\) \(\chi_{3971}(195,\cdot)\) \(\chi_{3971}(206,\cdot)\) \(\chi_{3971}(215,\cdot)\) \(\chi_{3971}(226,\cdot)\) \(\chi_{3971}(233,\cdot)\) \(\chi_{3971}(237,\cdot)\) \(\chi_{3971}(244,\cdot)\) \(\chi_{3971}(270,\cdot)\) \(\chi_{3971}(271,\cdot)\) \(\chi_{3971}(272,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{855})$ |
| Fixed field: | Number field defined by a degree 1710 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{70}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3971 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{529}{1710}\right)\) | \(e\left(\frac{86}{855}\right)\) | \(e\left(\frac{529}{855}\right)\) | \(e\left(\frac{488}{855}\right)\) | \(e\left(\frac{701}{1710}\right)\) | \(e\left(\frac{401}{570}\right)\) | \(e\left(\frac{529}{570}\right)\) | \(e\left(\frac{172}{855}\right)\) | \(e\left(\frac{301}{342}\right)\) | \(e\left(\frac{41}{57}\right)\) |