Basic properties
| Modulus: | \(8002\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4001}(160,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8002.n
\(\chi_{8002}(25,\cdot)\) \(\chi_{8002}(379,\cdot)\) \(\chi_{8002}(579,\cdot)\) \(\chi_{8002}(583,\cdot)\) \(\chi_{8002}(1735,\cdot)\) \(\chi_{8002}(1761,\cdot)\) \(\chi_{8002}(1773,\cdot)\) \(\chi_{8002}(1785,\cdot)\) \(\chi_{8002}(1873,\cdot)\) \(\chi_{8002}(2333,\cdot)\) \(\chi_{8002}(2545,\cdot)\) \(\chi_{8002}(2847,\cdot)\) \(\chi_{8002}(2977,\cdot)\) \(\chi_{8002}(3017,\cdot)\) \(\chi_{8002}(3347,\cdot)\) \(\chi_{8002}(3353,\cdot)\) \(\chi_{8002}(3651,\cdot)\) \(\chi_{8002}(3717,\cdot)\) \(\chi_{8002}(3841,\cdot)\) \(\chi_{8002}(3897,\cdot)\) \(\chi_{8002}(4105,\cdot)\) \(\chi_{8002}(4161,\cdot)\) \(\chi_{8002}(4285,\cdot)\) \(\chi_{8002}(4351,\cdot)\) \(\chi_{8002}(4649,\cdot)\) \(\chi_{8002}(4655,\cdot)\) \(\chi_{8002}(4985,\cdot)\) \(\chi_{8002}(5025,\cdot)\) \(\chi_{8002}(5155,\cdot)\) \(\chi_{8002}(5457,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\(3\) → \(e\left(\frac{91}{100}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8002 }(4161, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(-i\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{39}{100}\right)\) |