Basic properties
| Modulus: | \(3020\) | |
| Conductor: | \(3020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | 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 3020.cq
\(\chi_{3020}(43,\cdot)\) \(\chi_{3020}(47,\cdot)\) \(\chi_{3020}(103,\cdot)\) \(\chi_{3020}(187,\cdot)\) \(\chi_{3020}(267,\cdot)\) \(\chi_{3020}(287,\cdot)\) \(\chi_{3020}(307,\cdot)\) \(\chi_{3020}(323,\cdot)\) \(\chi_{3020}(327,\cdot)\) \(\chi_{3020}(347,\cdot)\) \(\chi_{3020}(423,\cdot)\) \(\chi_{3020}(447,\cdot)\) \(\chi_{3020}(463,\cdot)\) \(\chi_{3020}(487,\cdot)\) \(\chi_{3020}(527,\cdot)\) \(\chi_{3020}(543,\cdot)\) \(\chi_{3020}(643,\cdot)\) \(\chi_{3020}(647,\cdot)\) \(\chi_{3020}(703,\cdot)\) \(\chi_{3020}(707,\cdot)\) \(\chi_{3020}(743,\cdot)\) \(\chi_{3020}(843,\cdot)\) \(\chi_{3020}(923,\cdot)\) \(\chi_{3020}(927,\cdot)\) \(\chi_{3020}(943,\cdot)\) \(\chi_{3020}(1003,\cdot)\) \(\chi_{3020}(1027,\cdot)\) \(\chi_{3020}(1043,\cdot)\) \(\chi_{3020}(1067,\cdot)\) \(\chi_{3020}(1147,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((1511,2417,761)\) → \((-1,i,e\left(\frac{13}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3020 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{109}{300}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{119}{150}\right)\) | \(e\left(\frac{257}{300}\right)\) | \(e\left(\frac{91}{300}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{87}{100}\right)\) |