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 \(\chi_{1617}(365,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.by
\(\chi_{3234}(29,\cdot)\) \(\chi_{3234}(239,\cdot)\) \(\chi_{3234}(281,\cdot)\) \(\chi_{3234}(365,\cdot)\) \(\chi_{3234}(701,\cdot)\) \(\chi_{3234}(743,\cdot)\) \(\chi_{3234}(827,\cdot)\) \(\chi_{3234}(953,\cdot)\) \(\chi_{3234}(1163,\cdot)\) \(\chi_{3234}(1205,\cdot)\) \(\chi_{3234}(1289,\cdot)\) \(\chi_{3234}(1415,\cdot)\) \(\chi_{3234}(1625,\cdot)\) \(\chi_{3234}(1751,\cdot)\) \(\chi_{3234}(1877,\cdot)\) \(\chi_{3234}(2087,\cdot)\) \(\chi_{3234}(2129,\cdot)\) \(\chi_{3234}(2213,\cdot)\) \(\chi_{3234}(2339,\cdot)\) \(\chi_{3234}(2591,\cdot)\) \(\chi_{3234}(2675,\cdot)\) \(\chi_{3234}(2801,\cdot)\) \(\chi_{3234}(3011,\cdot)\) \(\chi_{3234}(3053,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,2059)\) → \((-1,e\left(\frac{4}{7}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(365, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) |