Basic properties
| Modulus: | \(5312\) | |
| Conductor: | \(5312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(656\) | 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 5312.bn
\(\chi_{5312}(21,\cdot)\) \(\chi_{5312}(29,\cdot)\) \(\chi_{5312}(37,\cdot)\) \(\chi_{5312}(61,\cdot)\) \(\chi_{5312}(69,\cdot)\) \(\chi_{5312}(77,\cdot)\) \(\chi_{5312}(93,\cdot)\) \(\chi_{5312}(109,\cdot)\) \(\chi_{5312}(173,\cdot)\) \(\chi_{5312}(189,\cdot)\) \(\chi_{5312}(197,\cdot)\) \(\chi_{5312}(229,\cdot)\) \(\chi_{5312}(253,\cdot)\) \(\chi_{5312}(261,\cdot)\) \(\chi_{5312}(277,\cdot)\) \(\chi_{5312}(285,\cdot)\) \(\chi_{5312}(293,\cdot)\) \(\chi_{5312}(317,\cdot)\) \(\chi_{5312}(341,\cdot)\) \(\chi_{5312}(349,\cdot)\) \(\chi_{5312}(357,\cdot)\) \(\chi_{5312}(365,\cdot)\) \(\chi_{5312}(373,\cdot)\) \(\chi_{5312}(381,\cdot)\) \(\chi_{5312}(397,\cdot)\) \(\chi_{5312}(413,\cdot)\) \(\chi_{5312}(445,\cdot)\) \(\chi_{5312}(453,\cdot)\) \(\chi_{5312}(485,\cdot)\) \(\chi_{5312}(493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{656})$ |
| Fixed field: | Number field defined by a degree 656 polynomial (not computed) |
Values on generators
\((831,3653,3073)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{40}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 5312 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{447}{656}\right)\) | \(e\left(\frac{101}{656}\right)\) | \(e\left(\frac{305}{328}\right)\) | \(e\left(\frac{119}{328}\right)\) | \(e\left(\frac{313}{656}\right)\) | \(e\left(\frac{203}{656}\right)\) | \(e\left(\frac{137}{164}\right)\) | \(e\left(\frac{63}{164}\right)\) | \(e\left(\frac{355}{656}\right)\) | \(e\left(\frac{401}{656}\right)\) |