Basic properties
Modulus: | \(7803\) | |
Conductor: | \(7803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(306\) | 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 7803.bx
\(\chi_{7803}(16,\cdot)\) \(\chi_{7803}(67,\cdot)\) \(\chi_{7803}(169,\cdot)\) \(\chi_{7803}(220,\cdot)\) \(\chi_{7803}(322,\cdot)\) \(\chi_{7803}(373,\cdot)\) \(\chi_{7803}(475,\cdot)\) \(\chi_{7803}(526,\cdot)\) \(\chi_{7803}(628,\cdot)\) \(\chi_{7803}(679,\cdot)\) \(\chi_{7803}(781,\cdot)\) \(\chi_{7803}(832,\cdot)\) \(\chi_{7803}(934,\cdot)\) \(\chi_{7803}(985,\cdot)\) \(\chi_{7803}(1087,\cdot)\) \(\chi_{7803}(1138,\cdot)\) \(\chi_{7803}(1240,\cdot)\) \(\chi_{7803}(1291,\cdot)\) \(\chi_{7803}(1393,\cdot)\) \(\chi_{7803}(1546,\cdot)\) \(\chi_{7803}(1597,\cdot)\) \(\chi_{7803}(1699,\cdot)\) \(\chi_{7803}(1750,\cdot)\) \(\chi_{7803}(1852,\cdot)\) \(\chi_{7803}(1903,\cdot)\) \(\chi_{7803}(2005,\cdot)\) \(\chi_{7803}(2056,\cdot)\) \(\chi_{7803}(2158,\cdot)\) \(\chi_{7803}(2209,\cdot)\) \(\chi_{7803}(2362,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{153})$ |
Fixed field: | Number field defined by a degree 306 polynomial (not computed) |
Values on generators
\((2891,2026)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{27}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 7803 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{153}\right)\) | \(e\left(\frac{32}{153}\right)\) | \(e\left(\frac{295}{306}\right)\) | \(e\left(\frac{197}{306}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{47}{306}\right)\) | \(e\left(\frac{65}{153}\right)\) | \(e\left(\frac{229}{306}\right)\) | \(e\left(\frac{64}{153}\right)\) |