Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(75\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{151}(62,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8003.bk
\(\chi_{8003}(213,\cdot)\) \(\chi_{8003}(319,\cdot)\) \(\chi_{8003}(478,\cdot)\) \(\chi_{8003}(743,\cdot)\) \(\chi_{8003}(955,\cdot)\) \(\chi_{8003}(1697,\cdot)\) \(\chi_{8003}(1909,\cdot)\) \(\chi_{8003}(2386,\cdot)\) \(\chi_{8003}(2598,\cdot)\) \(\chi_{8003}(2704,\cdot)\) \(\chi_{8003}(2757,\cdot)\) \(\chi_{8003}(2863,\cdot)\) \(\chi_{8003}(2916,\cdot)\) \(\chi_{8003}(2969,\cdot)\) \(\chi_{8003}(3075,\cdot)\) \(\chi_{8003}(3181,\cdot)\) \(\chi_{8003}(3287,\cdot)\) \(\chi_{8003}(3340,\cdot)\) \(\chi_{8003}(3658,\cdot)\) \(\chi_{8003}(3817,\cdot)\) \(\chi_{8003}(3870,\cdot)\) \(\chi_{8003}(4029,\cdot)\) \(\chi_{8003}(4082,\cdot)\) \(\chi_{8003}(4135,\cdot)\) \(\chi_{8003}(4400,\cdot)\) \(\chi_{8003}(4453,\cdot)\) \(\chi_{8003}(4718,\cdot)\) \(\chi_{8003}(4771,\cdot)\) \(\chi_{8003}(4877,\cdot)\) \(\chi_{8003}(5354,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\((4984,7103)\) → \((1,e\left(\frac{49}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(213, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{75}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{58}{75}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{68}{75}\right)\) | \(e\left(\frac{31}{75}\right)\) |