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.be
\(\chi_{2151}(2,\cdot)\) \(\chi_{2151}(5,\cdot)\) \(\chi_{2151}(11,\cdot)\) \(\chi_{2151}(20,\cdot)\) \(\chi_{2151}(29,\cdot)\) \(\chi_{2151}(32,\cdot)\) \(\chi_{2151}(50,\cdot)\) \(\chi_{2151}(68,\cdot)\) \(\chi_{2151}(83,\cdot)\) \(\chi_{2151}(110,\cdot)\) \(\chi_{2151}(113,\cdot)\) \(\chi_{2151}(122,\cdot)\) \(\chi_{2151}(155,\cdot)\) \(\chi_{2151}(176,\cdot)\) \(\chi_{2151}(182,\cdot)\) \(\chi_{2151}(200,\cdot)\) \(\chi_{2151}(218,\cdot)\) \(\chi_{2151}(248,\cdot)\) \(\chi_{2151}(254,\cdot)\) \(\chi_{2151}(257,\cdot)\) \(\chi_{2151}(266,\cdot)\) \(\chi_{2151}(272,\cdot)\) \(\chi_{2151}(284,\cdot)\) \(\chi_{2151}(293,\cdot)\) \(\chi_{2151}(299,\cdot)\) \(\chi_{2151}(311,\cdot)\) \(\chi_{2151}(320,\cdot)\) \(\chi_{2151}(326,\cdot)\) \(\chi_{2151}(329,\cdot)\) \(\chi_{2151}(335,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{357})$ |
| Fixed field: | Number field defined by a degree 714 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{80}{119}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{383}{714}\right)\) | \(e\left(\frac{26}{357}\right)\) | \(e\left(\frac{433}{714}\right)\) | \(e\left(\frac{121}{357}\right)\) | \(e\left(\frac{145}{238}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{611}{714}\right)\) | \(e\left(\frac{86}{357}\right)\) | \(e\left(\frac{625}{714}\right)\) | \(e\left(\frac{52}{357}\right)\) |