Basic properties
| Modulus: | \(3020\) | |
| Conductor: | \(755\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{755}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3020.cs
\(\chi_{3020}(13,\cdot)\) \(\chi_{3020}(77,\cdot)\) \(\chi_{3020}(93,\cdot)\) \(\chi_{3020}(117,\cdot)\) \(\chi_{3020}(133,\cdot)\) \(\chi_{3020}(157,\cdot)\) \(\chi_{3020}(233,\cdot)\) \(\chi_{3020}(253,\cdot)\) \(\chi_{3020}(257,\cdot)\) \(\chi_{3020}(277,\cdot)\) \(\chi_{3020}(297,\cdot)\) \(\chi_{3020}(317,\cdot)\) \(\chi_{3020}(337,\cdot)\) \(\chi_{3020}(353,\cdot)\) \(\chi_{3020}(373,\cdot)\) \(\chi_{3020}(413,\cdot)\) \(\chi_{3020}(417,\cdot)\) \(\chi_{3020}(557,\cdot)\) \(\chi_{3020}(573,\cdot)\) \(\chi_{3020}(593,\cdot)\) \(\chi_{3020}(617,\cdot)\) \(\chi_{3020}(693,\cdot)\) \(\chi_{3020}(697,\cdot)\) \(\chi_{3020}(713,\cdot)\) \(\chi_{3020}(733,\cdot)\) \(\chi_{3020}(737,\cdot)\) \(\chi_{3020}(837,\cdot)\) \(\chi_{3020}(857,\cdot)\) \(\chi_{3020}(913,\cdot)\) \(\chi_{3020}(957,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((1511,2417,761)\) → \((1,-i,e\left(\frac{41}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3020 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{19}{300}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{52}{75}\right)\) | \(e\left(\frac{137}{300}\right)\) | \(e\left(\frac{181}{300}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{34}{75}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{17}{100}\right)\) |