Basic properties
| Modulus: | \(3234\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1617}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.cd
\(\chi_{3234}(41,\cdot)\) \(\chi_{3234}(83,\cdot)\) \(\chi_{3234}(167,\cdot)\) \(\chi_{3234}(503,\cdot)\) \(\chi_{3234}(545,\cdot)\) \(\chi_{3234}(629,\cdot)\) \(\chi_{3234}(755,\cdot)\) \(\chi_{3234}(965,\cdot)\) \(\chi_{3234}(1007,\cdot)\) \(\chi_{3234}(1091,\cdot)\) \(\chi_{3234}(1217,\cdot)\) \(\chi_{3234}(1427,\cdot)\) \(\chi_{3234}(1553,\cdot)\) \(\chi_{3234}(1679,\cdot)\) \(\chi_{3234}(1889,\cdot)\) \(\chi_{3234}(1931,\cdot)\) \(\chi_{3234}(2015,\cdot)\) \(\chi_{3234}(2141,\cdot)\) \(\chi_{3234}(2393,\cdot)\) \(\chi_{3234}(2477,\cdot)\) \(\chi_{3234}(2603,\cdot)\) \(\chi_{3234}(2813,\cdot)\) \(\chi_{3234}(2855,\cdot)\) \(\chi_{3234}(3065,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,2059)\) → \((-1,e\left(\frac{3}{14}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3234 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) |