Basic properties
| Modulus: | \(6675\) | |
| Conductor: | \(1335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1335}(794,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6675.cz
\(\chi_{6675}(74,\cdot)\) \(\chi_{6675}(149,\cdot)\) \(\chi_{6675}(224,\cdot)\) \(\chi_{6675}(599,\cdot)\) \(\chi_{6675}(674,\cdot)\) \(\chi_{6675}(824,\cdot)\) \(\chi_{6675}(1049,\cdot)\) \(\chi_{6675}(1124,\cdot)\) \(\chi_{6675}(1274,\cdot)\) \(\chi_{6675}(1349,\cdot)\) \(\chi_{6675}(1499,\cdot)\) \(\chi_{6675}(1574,\cdot)\) \(\chi_{6675}(1724,\cdot)\) \(\chi_{6675}(1799,\cdot)\) \(\chi_{6675}(2024,\cdot)\) \(\chi_{6675}(2174,\cdot)\) \(\chi_{6675}(2249,\cdot)\) \(\chi_{6675}(2624,\cdot)\) \(\chi_{6675}(2699,\cdot)\) \(\chi_{6675}(2774,\cdot)\) \(\chi_{6675}(2924,\cdot)\) \(\chi_{6675}(2999,\cdot)\) \(\chi_{6675}(3074,\cdot)\) \(\chi_{6675}(3299,\cdot)\) \(\chi_{6675}(3824,\cdot)\) \(\chi_{6675}(3974,\cdot)\) \(\chi_{6675}(4124,\cdot)\) \(\chi_{6675}(4424,\cdot)\) \(\chi_{6675}(4574,\cdot)\) \(\chi_{6675}(4724,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((4451,802,2851)\) → \((-1,-1,e\left(\frac{37}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6675 }(4799, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{63}{88}\right)\) |