Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2005}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8020.dy
\(\chi_{8020}(17,\cdot)\) \(\chi_{8020}(53,\cdot)\) \(\chi_{8020}(97,\cdot)\) \(\chi_{8020}(233,\cdot)\) \(\chi_{8020}(277,\cdot)\) \(\chi_{8020}(377,\cdot)\) \(\chi_{8020}(413,\cdot)\) \(\chi_{8020}(497,\cdot)\) \(\chi_{8020}(553,\cdot)\) \(\chi_{8020}(593,\cdot)\) \(\chi_{8020}(637,\cdot)\) \(\chi_{8020}(697,\cdot)\) \(\chi_{8020}(717,\cdot)\) \(\chi_{8020}(737,\cdot)\) \(\chi_{8020}(873,\cdot)\) \(\chi_{8020}(893,\cdot)\) \(\chi_{8020}(897,\cdot)\) \(\chi_{8020}(917,\cdot)\) \(\chi_{8020}(933,\cdot)\) \(\chi_{8020}(937,\cdot)\) \(\chi_{8020}(993,\cdot)\) \(\chi_{8020}(1013,\cdot)\) \(\chi_{8020}(1033,\cdot)\) \(\chi_{8020}(1073,\cdot)\) \(\chi_{8020}(1097,\cdot)\) \(\chi_{8020}(1197,\cdot)\) \(\chi_{8020}(1277,\cdot)\) \(\chi_{8020}(1333,\cdot)\) \(\chi_{8020}(1337,\cdot)\) \(\chi_{8020}(1373,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((4011,6417,7221)\) → \((1,i,e\left(\frac{383}{400}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{283}{400}\right)\) | \(e\left(\frac{123}{200}\right)\) | \(e\left(\frac{83}{200}\right)\) | \(e\left(\frac{151}{200}\right)\) | \(e\left(\frac{77}{400}\right)\) | \(e\left(\frac{389}{400}\right)\) | \(e\left(\frac{229}{400}\right)\) | \(e\left(\frac{129}{400}\right)\) | \(e\left(\frac{153}{400}\right)\) | \(e\left(\frac{49}{400}\right)\) |