Basic properties
| Modulus: | \(15030\) | |
| Conductor: | \(7515\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(996\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7515}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 15030.bt
\(\chi_{15030}(23,\cdot)\) \(\chi_{15030}(83,\cdot)\) \(\chi_{15030}(113,\cdot)\) \(\chi_{15030}(227,\cdot)\) \(\chi_{15030}(257,\cdot)\) \(\chi_{15030}(347,\cdot)\) \(\chi_{15030}(407,\cdot)\) \(\chi_{15030}(437,\cdot)\) \(\chi_{15030}(443,\cdot)\) \(\chi_{15030}(473,\cdot)\) \(\chi_{15030}(497,\cdot)\) \(\chi_{15030}(527,\cdot)\) \(\chi_{15030}(587,\cdot)\) \(\chi_{15030}(707,\cdot)\) \(\chi_{15030}(713,\cdot)\) \(\chi_{15030}(797,\cdot)\) \(\chi_{15030}(803,\cdot)\) \(\chi_{15030}(833,\cdot)\) \(\chi_{15030}(887,\cdot)\) \(\chi_{15030}(977,\cdot)\) \(\chi_{15030}(983,\cdot)\) \(\chi_{15030}(1037,\cdot)\) \(\chi_{15030}(1073,\cdot)\) \(\chi_{15030}(1103,\cdot)\) \(\chi_{15030}(1127,\cdot)\) \(\chi_{15030}(1157,\cdot)\) \(\chi_{15030}(1163,\cdot)\) \(\chi_{15030}(1247,\cdot)\) \(\chi_{15030}(1307,\cdot)\) \(\chi_{15030}(1373,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{996})$ |
| Fixed field: | Number field defined by a degree 996 polynomial (not computed) |
Values on generators
\((3341,3007,4681)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{73}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 15030 }(113, a) \) | \(-1\) | \(1\) | \(e\left(\frac{971}{996}\right)\) | \(e\left(\frac{73}{498}\right)\) | \(e\left(\frac{211}{996}\right)\) | \(e\left(\frac{185}{332}\right)\) | \(e\left(\frac{1}{166}\right)\) | \(e\left(\frac{949}{996}\right)\) | \(e\left(\frac{74}{249}\right)\) | \(e\left(\frac{61}{249}\right)\) | \(e\left(\frac{191}{332}\right)\) | \(e\left(\frac{205}{249}\right)\) |