Basic properties
Modulus: | \(3234\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{539}(85,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.cb
\(\chi_{3234}(85,\cdot)\) \(\chi_{3234}(127,\cdot)\) \(\chi_{3234}(211,\cdot)\) \(\chi_{3234}(337,\cdot)\) \(\chi_{3234}(547,\cdot)\) \(\chi_{3234}(673,\cdot)\) \(\chi_{3234}(799,\cdot)\) \(\chi_{3234}(1009,\cdot)\) \(\chi_{3234}(1051,\cdot)\) \(\chi_{3234}(1135,\cdot)\) \(\chi_{3234}(1261,\cdot)\) \(\chi_{3234}(1513,\cdot)\) \(\chi_{3234}(1597,\cdot)\) \(\chi_{3234}(1723,\cdot)\) \(\chi_{3234}(1933,\cdot)\) \(\chi_{3234}(1975,\cdot)\) \(\chi_{3234}(2185,\cdot)\) \(\chi_{3234}(2395,\cdot)\) \(\chi_{3234}(2437,\cdot)\) \(\chi_{3234}(2521,\cdot)\) \(\chi_{3234}(2857,\cdot)\) \(\chi_{3234}(2899,\cdot)\) \(\chi_{3234}(2983,\cdot)\) \(\chi_{3234}(3109,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,2059)\) → \((1,e\left(\frac{2}{7}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(85, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) |