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 \(\chi_{539}(370,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.ca
\(\chi_{3234}(13,\cdot)\) \(\chi_{3234}(139,\cdot)\) \(\chi_{3234}(349,\cdot)\) \(\chi_{3234}(475,\cdot)\) \(\chi_{3234}(601,\cdot)\) \(\chi_{3234}(811,\cdot)\) \(\chi_{3234}(853,\cdot)\) \(\chi_{3234}(937,\cdot)\) \(\chi_{3234}(1063,\cdot)\) \(\chi_{3234}(1315,\cdot)\) \(\chi_{3234}(1399,\cdot)\) \(\chi_{3234}(1525,\cdot)\) \(\chi_{3234}(1735,\cdot)\) \(\chi_{3234}(1777,\cdot)\) \(\chi_{3234}(1987,\cdot)\) \(\chi_{3234}(2197,\cdot)\) \(\chi_{3234}(2239,\cdot)\) \(\chi_{3234}(2323,\cdot)\) \(\chi_{3234}(2659,\cdot)\) \(\chi_{3234}(2701,\cdot)\) \(\chi_{3234}(2785,\cdot)\) \(\chi_{3234}(2911,\cdot)\) \(\chi_{3234}(3121,\cdot)\) \(\chi_{3234}(3163,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,2059)\) → \((1,e\left(\frac{1}{14}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(1987, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) |