Basic properties
| Modulus: | \(7803\) | |
| Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{867}(80,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7803.bu
\(\chi_{7803}(80,\cdot)\) \(\chi_{7803}(107,\cdot)\) \(\chi_{7803}(215,\cdot)\) \(\chi_{7803}(269,\cdot)\) \(\chi_{7803}(296,\cdot)\) \(\chi_{7803}(350,\cdot)\) \(\chi_{7803}(377,\cdot)\) \(\chi_{7803}(431,\cdot)\) \(\chi_{7803}(539,\cdot)\) \(\chi_{7803}(566,\cdot)\) \(\chi_{7803}(674,\cdot)\) \(\chi_{7803}(728,\cdot)\) \(\chi_{7803}(755,\cdot)\) \(\chi_{7803}(809,\cdot)\) \(\chi_{7803}(836,\cdot)\) \(\chi_{7803}(890,\cdot)\) \(\chi_{7803}(1133,\cdot)\) \(\chi_{7803}(1187,\cdot)\) \(\chi_{7803}(1214,\cdot)\) \(\chi_{7803}(1268,\cdot)\) \(\chi_{7803}(1295,\cdot)\) \(\chi_{7803}(1349,\cdot)\) \(\chi_{7803}(1457,\cdot)\) \(\chi_{7803}(1484,\cdot)\) \(\chi_{7803}(1592,\cdot)\) \(\chi_{7803}(1646,\cdot)\) \(\chi_{7803}(1673,\cdot)\) \(\chi_{7803}(1727,\cdot)\) \(\chi_{7803}(1754,\cdot)\) \(\chi_{7803}(1808,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2891,2026)\) → \((-1,e\left(\frac{173}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 7803 }(80, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{136}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{41}{272}\right)\) | \(e\left(\frac{159}{272}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{135}{272}\right)\) | \(e\left(\frac{35}{272}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{253}{272}\right)\) | \(e\left(\frac{13}{34}\right)\) |