Basic properties
Modulus: | \(4029\) | |
Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(208\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1343}(703,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.ct
\(\chi_{4029}(58,\cdot)\) \(\chi_{4029}(61,\cdot)\) \(\chi_{4029}(91,\cdot)\) \(\chi_{4029}(112,\cdot)\) \(\chi_{4029}(148,\cdot)\) \(\chi_{4029}(175,\cdot)\) \(\chi_{4029}(199,\cdot)\) \(\chi_{4029}(295,\cdot)\) \(\chi_{4029}(328,\cdot)\) \(\chi_{4029}(343,\cdot)\) \(\chi_{4029}(385,\cdot)\) \(\chi_{4029}(436,\cdot)\) \(\chi_{4029}(466,\cdot)\) \(\chi_{4029}(532,\cdot)\) \(\chi_{4029}(568,\cdot)\) \(\chi_{4029}(622,\cdot)\) \(\chi_{4029}(649,\cdot)\) \(\chi_{4029}(673,\cdot)\) \(\chi_{4029}(703,\cdot)\) \(\chi_{4029}(772,\cdot)\) \(\chi_{4029}(802,\cdot)\) \(\chi_{4029}(805,\cdot)\) \(\chi_{4029}(823,\cdot)\) \(\chi_{4029}(847,\cdot)\) \(\chi_{4029}(940,\cdot)\) \(\chi_{4029}(1006,\cdot)\) \(\chi_{4029}(1009,\cdot)\) \(\chi_{4029}(1042,\cdot)\) \(\chi_{4029}(1060,\cdot)\) \(\chi_{4029}(1246,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{208})$ |
Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{17}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(703, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{104}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{47}{208}\right)\) | \(e\left(\frac{201}{208}\right)\) | \(e\left(\frac{23}{104}\right)\) | \(e\left(\frac{201}{208}\right)\) | \(e\left(\frac{5}{208}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{147}{208}\right)\) | \(e\left(\frac{25}{26}\right)\) |