Basic properties
| Modulus: | \(3789\) | |
| Conductor: | \(421\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{421}(379,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3789.du
\(\chi_{3789}(10,\cdot)\) \(\chi_{3789}(19,\cdot)\) \(\chi_{3789}(37,\cdot)\) \(\chi_{3789}(91,\cdot)\) \(\chi_{3789}(127,\cdot)\) \(\chi_{3789}(172,\cdot)\) \(\chi_{3789}(298,\cdot)\) \(\chi_{3789}(352,\cdot)\) \(\chi_{3789}(379,\cdot)\) \(\chi_{3789}(550,\cdot)\) \(\chi_{3789}(685,\cdot)\) \(\chi_{3789}(901,\cdot)\) \(\chi_{3789}(1000,\cdot)\) \(\chi_{3789}(1045,\cdot)\) \(\chi_{3789}(1099,\cdot)\) \(\chi_{3789}(1207,\cdot)\) \(\chi_{3789}(1216,\cdot)\) \(\chi_{3789}(1324,\cdot)\) \(\chi_{3789}(1396,\cdot)\) \(\chi_{3789}(1972,\cdot)\) \(\chi_{3789}(2044,\cdot)\) \(\chi_{3789}(2152,\cdot)\) \(\chi_{3789}(2161,\cdot)\) \(\chi_{3789}(2269,\cdot)\) \(\chi_{3789}(2323,\cdot)\) \(\chi_{3789}(2368,\cdot)\) \(\chi_{3789}(2467,\cdot)\) \(\chi_{3789}(2683,\cdot)\) \(\chi_{3789}(2818,\cdot)\) \(\chi_{3789}(2989,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1685,2107)\) → \((1,e\left(\frac{47}{140}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3789 }(379, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{12}{35}\right)\) |