Basic properties
| Modulus: | \(2151\) | |
| Conductor: | \(2151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(714\) | 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 2151.bd
\(\chi_{2151}(7,\cdot)\) \(\chi_{2151}(13,\cdot)\) \(\chi_{2151}(43,\cdot)\) \(\chi_{2151}(70,\cdot)\) \(\chi_{2151}(79,\cdot)\) \(\chi_{2151}(94,\cdot)\) \(\chi_{2151}(97,\cdot)\) \(\chi_{2151}(103,\cdot)\) \(\chi_{2151}(106,\cdot)\) \(\chi_{2151}(112,\cdot)\) \(\chi_{2151}(115,\cdot)\) \(\chi_{2151}(130,\cdot)\) \(\chi_{2151}(148,\cdot)\) \(\chi_{2151}(151,\cdot)\) \(\chi_{2151}(175,\cdot)\) \(\chi_{2151}(178,\cdot)\) \(\chi_{2151}(184,\cdot)\) \(\chi_{2151}(205,\cdot)\) \(\chi_{2151}(214,\cdot)\) \(\chi_{2151}(223,\cdot)\) \(\chi_{2151}(265,\cdot)\) \(\chi_{2151}(274,\cdot)\) \(\chi_{2151}(286,\cdot)\) \(\chi_{2151}(292,\cdot)\) \(\chi_{2151}(295,\cdot)\) \(\chi_{2151}(304,\cdot)\) \(\chi_{2151}(313,\cdot)\) \(\chi_{2151}(328,\cdot)\) \(\chi_{2151}(331,\cdot)\) \(\chi_{2151}(358,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{357})$ |
| Fixed field: | Number field defined by a degree 714 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{15}{238}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{295}{357}\right)\) | \(e\left(\frac{233}{357}\right)\) | \(e\left(\frac{11}{357}\right)\) | \(e\left(\frac{521}{714}\right)\) | \(e\left(\frac{57}{119}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{328}{357}\right)\) | \(e\left(\frac{31}{714}\right)\) | \(e\left(\frac{397}{714}\right)\) | \(e\left(\frac{109}{357}\right)\) |