Basic properties
| Modulus: | \(2151\) | |
| Conductor: | \(2151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(357\) | 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 2151.bc
\(\chi_{2151}(4,\cdot)\) \(\chi_{2151}(16,\cdot)\) \(\chi_{2151}(25,\cdot)\) \(\chi_{2151}(31,\cdot)\) \(\chi_{2151}(34,\cdot)\) \(\chi_{2151}(49,\cdot)\) \(\chi_{2151}(58,\cdot)\) \(\chi_{2151}(61,\cdot)\) \(\chi_{2151}(85,\cdot)\) \(\chi_{2151}(88,\cdot)\) \(\chi_{2151}(121,\cdot)\) \(\chi_{2151}(124,\cdot)\) \(\chi_{2151}(133,\cdot)\) \(\chi_{2151}(142,\cdot)\) \(\chi_{2151}(157,\cdot)\) \(\chi_{2151}(160,\cdot)\) \(\chi_{2151}(169,\cdot)\) \(\chi_{2151}(193,\cdot)\) \(\chi_{2151}(196,\cdot)\) \(\chi_{2151}(202,\cdot)\) \(\chi_{2151}(220,\cdot)\) \(\chi_{2151}(232,\cdot)\) \(\chi_{2151}(241,\cdot)\) \(\chi_{2151}(247,\cdot)\) \(\chi_{2151}(250,\cdot)\) \(\chi_{2151}(256,\cdot)\) \(\chi_{2151}(259,\cdot)\) \(\chi_{2151}(268,\cdot)\) \(\chi_{2151}(301,\cdot)\) \(\chi_{2151}(319,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{357})$ |
| Fixed field: | Number field defined by a degree 357 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{13}{119}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{313}{357}\right)\) | \(e\left(\frac{269}{357}\right)\) | \(e\left(\frac{146}{357}\right)\) | \(e\left(\frac{277}{357}\right)\) | \(e\left(\frac{75}{119}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{37}{357}\right)\) | \(e\left(\frac{11}{357}\right)\) | \(e\left(\frac{233}{357}\right)\) | \(e\left(\frac{181}{357}\right)\) |