Basic properties
| Modulus: | \(629\) | |
| Conductor: | \(629\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | 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 629.cb
\(\chi_{629}(3,\cdot)\) \(\chi_{629}(28,\cdot)\) \(\chi_{629}(40,\cdot)\) \(\chi_{629}(41,\cdot)\) \(\chi_{629}(58,\cdot)\) \(\chi_{629}(62,\cdot)\) \(\chi_{629}(65,\cdot)\) \(\chi_{629}(78,\cdot)\) \(\chi_{629}(95,\cdot)\) \(\chi_{629}(99,\cdot)\) \(\chi_{629}(114,\cdot)\) \(\chi_{629}(139,\cdot)\) \(\chi_{629}(141,\cdot)\) \(\chi_{629}(173,\cdot)\) \(\chi_{629}(176,\cdot)\) \(\chi_{629}(210,\cdot)\) \(\chi_{629}(215,\cdot)\) \(\chi_{629}(226,\cdot)\) \(\chi_{629}(243,\cdot)\) \(\chi_{629}(250,\cdot)\) \(\chi_{629}(252,\cdot)\) \(\chi_{629}(262,\cdot)\) \(\chi_{629}(284,\cdot)\) \(\chi_{629}(299,\cdot)\) \(\chi_{629}(300,\cdot)\) \(\chi_{629}(317,\cdot)\) \(\chi_{629}(326,\cdot)\) \(\chi_{629}(337,\cdot)\) \(\chi_{629}(354,\cdot)\) \(\chi_{629}(363,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((445,409)\) → \((e\left(\frac{11}{16}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 629 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{83}{144}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{71}{144}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{17}{144}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{7}{48}\right)\) |