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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2151.bf
\(\chi_{2151}(14,\cdot)\) \(\chi_{2151}(41,\cdot)\) \(\chi_{2151}(47,\cdot)\) \(\chi_{2151}(56,\cdot)\) \(\chi_{2151}(59,\cdot)\) \(\chi_{2151}(65,\cdot)\) \(\chi_{2151}(74,\cdot)\) \(\chi_{2151}(77,\cdot)\) \(\chi_{2151}(86,\cdot)\) \(\chi_{2151}(92,\cdot)\) \(\chi_{2151}(95,\cdot)\) \(\chi_{2151}(104,\cdot)\) \(\chi_{2151}(119,\cdot)\) \(\chi_{2151}(131,\cdot)\) \(\chi_{2151}(137,\cdot)\) \(\chi_{2151}(140,\cdot)\) \(\chi_{2151}(146,\cdot)\) \(\chi_{2151}(149,\cdot)\) \(\chi_{2151}(158,\cdot)\) \(\chi_{2151}(167,\cdot)\) \(\chi_{2151}(173,\cdot)\) \(\chi_{2151}(185,\cdot)\) \(\chi_{2151}(191,\cdot)\) \(\chi_{2151}(194,\cdot)\) \(\chi_{2151}(209,\cdot)\) \(\chi_{2151}(212,\cdot)\) \(\chi_{2151}(221,\cdot)\) \(\chi_{2151}(227,\cdot)\) \(\chi_{2151}(230,\cdot)\) \(\chi_{2151}(236,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{357})$ |
| Fixed field: | Number field defined by a degree 714 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{113}{238}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{359}{714}\right)\) | \(e\left(\frac{2}{357}\right)\) | \(e\left(\frac{253}{714}\right)\) | \(e\left(\frac{101}{714}\right)\) | \(e\left(\frac{121}{238}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{47}{714}\right)\) | \(e\left(\frac{535}{714}\right)\) | \(e\left(\frac{230}{357}\right)\) | \(e\left(\frac{4}{357}\right)\) |