Basic properties
Modulus: | \(5915\) | |
Conductor: | \(5915\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5915.hq
\(\chi_{5915}(37,\cdot)\) \(\chi_{5915}(93,\cdot)\) \(\chi_{5915}(123,\cdot)\) \(\chi_{5915}(137,\cdot)\) \(\chi_{5915}(492,\cdot)\) \(\chi_{5915}(548,\cdot)\) \(\chi_{5915}(578,\cdot)\) \(\chi_{5915}(592,\cdot)\) \(\chi_{5915}(947,\cdot)\) \(\chi_{5915}(1003,\cdot)\) \(\chi_{5915}(1047,\cdot)\) \(\chi_{5915}(1402,\cdot)\) \(\chi_{5915}(1458,\cdot)\) \(\chi_{5915}(1488,\cdot)\) \(\chi_{5915}(1857,\cdot)\) \(\chi_{5915}(1913,\cdot)\) \(\chi_{5915}(1943,\cdot)\) \(\chi_{5915}(1957,\cdot)\) \(\chi_{5915}(2312,\cdot)\) \(\chi_{5915}(2368,\cdot)\) \(\chi_{5915}(2398,\cdot)\) \(\chi_{5915}(2412,\cdot)\) \(\chi_{5915}(2767,\cdot)\) \(\chi_{5915}(2823,\cdot)\) \(\chi_{5915}(2853,\cdot)\) \(\chi_{5915}(2867,\cdot)\) \(\chi_{5915}(3222,\cdot)\) \(\chi_{5915}(3278,\cdot)\) \(\chi_{5915}(3308,\cdot)\) \(\chi_{5915}(3322,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,5071,1016)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{151}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(16\) | \(17\) |
\( \chi_{ 5915 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{47}{52}\right)\) |