Basic properties
| Modulus: | \(3215\) | |
| Conductor: | \(3215\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1284\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3215.w
\(\chi_{3215}(13,\cdot)\) \(\chi_{3215}(17,\cdot)\) \(\chi_{3215}(37,\cdot)\) \(\chi_{3215}(47,\cdot)\) \(\chi_{3215}(52,\cdot)\) \(\chi_{3215}(58,\cdot)\) \(\chi_{3215}(62,\cdot)\) \(\chi_{3215}(68,\cdot)\) \(\chi_{3215}(73,\cdot)\) \(\chi_{3215}(78,\cdot)\) \(\chi_{3215}(87,\cdot)\) \(\chi_{3215}(93,\cdot)\) \(\chi_{3215}(98,\cdot)\) \(\chi_{3215}(102,\cdot)\) \(\chi_{3215}(113,\cdot)\) \(\chi_{3215}(117,\cdot)\) \(\chi_{3215}(133,\cdot)\) \(\chi_{3215}(137,\cdot)\) \(\chi_{3215}(147,\cdot)\) \(\chi_{3215}(148,\cdot)\) \(\chi_{3215}(153,\cdot)\) \(\chi_{3215}(188,\cdot)\) \(\chi_{3215}(197,\cdot)\) \(\chi_{3215}(202,\cdot)\) \(\chi_{3215}(208,\cdot)\) \(\chi_{3215}(222,\cdot)\) \(\chi_{3215}(223,\cdot)\) \(\chi_{3215}(227,\cdot)\) \(\chi_{3215}(232,\cdot)\) \(\chi_{3215}(242,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1284})$ |
| Fixed field: | Number field defined by a degree 1284 polynomial (not computed) |
Values on generators
\((1287,11)\) → \((i,e\left(\frac{61}{642}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 3215 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{125}{428}\right)\) | \(e\left(\frac{47}{428}\right)\) | \(e\left(\frac{125}{214}\right)\) | \(e\left(\frac{43}{107}\right)\) | \(e\left(\frac{781}{1284}\right)\) | \(e\left(\frac{375}{428}\right)\) | \(e\left(\frac{47}{214}\right)\) | \(e\left(\frac{61}{642}\right)\) | \(e\left(\frac{297}{428}\right)\) | \(e\left(\frac{1201}{1284}\right)\) |