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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 629.bz
\(\chi_{629}(5,\cdot)\) \(\chi_{629}(22,\cdot)\) \(\chi_{629}(24,\cdot)\) \(\chi_{629}(54,\cdot)\) \(\chi_{629}(56,\cdot)\) \(\chi_{629}(57,\cdot)\) \(\chi_{629}(61,\cdot)\) \(\chi_{629}(92,\cdot)\) \(\chi_{629}(113,\cdot)\) \(\chi_{629}(116,\cdot)\) \(\chi_{629}(124,\cdot)\) \(\chi_{629}(126,\cdot)\) \(\chi_{629}(129,\cdot)\) \(\chi_{629}(133,\cdot)\) \(\chi_{629}(143,\cdot)\) \(\chi_{629}(163,\cdot)\) \(\chi_{629}(165,\cdot)\) \(\chi_{629}(167,\cdot)\) \(\chi_{629}(180,\cdot)\) \(\chi_{629}(190,\cdot)\) \(\chi_{629}(207,\cdot)\) \(\chi_{629}(235,\cdot)\) \(\chi_{629}(241,\cdot)\) \(\chi_{629}(261,\cdot)\) \(\chi_{629}(279,\cdot)\) \(\chi_{629}(283,\cdot)\) \(\chi_{629}(294,\cdot)\) \(\chi_{629}(301,\cdot)\) \(\chi_{629}(309,\cdot)\) \(\chi_{629}(316,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((445,409)\) → \((e\left(\frac{1}{16}\right),e\left(\frac{23}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 629 }(190, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{97}{144}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{144}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{19}{144}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{29}{48}\right)\) |