Basic properties
Modulus: | \(3234\) | |
Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1617}(482,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.cc
\(\chi_{3234}(125,\cdot)\) \(\chi_{3234}(251,\cdot)\) \(\chi_{3234}(335,\cdot)\) \(\chi_{3234}(377,\cdot)\) \(\chi_{3234}(713,\cdot)\) \(\chi_{3234}(797,\cdot)\) \(\chi_{3234}(839,\cdot)\) \(\chi_{3234}(1049,\cdot)\) \(\chi_{3234}(1259,\cdot)\) \(\chi_{3234}(1301,\cdot)\) \(\chi_{3234}(1511,\cdot)\) \(\chi_{3234}(1637,\cdot)\) \(\chi_{3234}(1721,\cdot)\) \(\chi_{3234}(1973,\cdot)\) \(\chi_{3234}(2099,\cdot)\) \(\chi_{3234}(2183,\cdot)\) \(\chi_{3234}(2225,\cdot)\) \(\chi_{3234}(2435,\cdot)\) \(\chi_{3234}(2561,\cdot)\) \(\chi_{3234}(2687,\cdot)\) \(\chi_{3234}(2897,\cdot)\) \(\chi_{3234}(3023,\cdot)\) \(\chi_{3234}(3107,\cdot)\) \(\chi_{3234}(3149,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,2059)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(2099, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) |