Basic properties
Modulus: | \(5472\) | |
Conductor: | \(5472\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | 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 5472.jd
\(\chi_{5472}(85,\cdot)\) \(\chi_{5472}(517,\cdot)\) \(\chi_{5472}(853,\cdot)\) \(\chi_{5472}(1069,\cdot)\) \(\chi_{5472}(1165,\cdot)\) \(\chi_{5472}(1213,\cdot)\) \(\chi_{5472}(1453,\cdot)\) \(\chi_{5472}(1885,\cdot)\) \(\chi_{5472}(2221,\cdot)\) \(\chi_{5472}(2437,\cdot)\) \(\chi_{5472}(2533,\cdot)\) \(\chi_{5472}(2581,\cdot)\) \(\chi_{5472}(2821,\cdot)\) \(\chi_{5472}(3253,\cdot)\) \(\chi_{5472}(3589,\cdot)\) \(\chi_{5472}(3805,\cdot)\) \(\chi_{5472}(3901,\cdot)\) \(\chi_{5472}(3949,\cdot)\) \(\chi_{5472}(4189,\cdot)\) \(\chi_{5472}(4621,\cdot)\) \(\chi_{5472}(4957,\cdot)\) \(\chi_{5472}(5173,\cdot)\) \(\chi_{5472}(5269,\cdot)\) \(\chi_{5472}(5317,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4447,2053,1217,3745)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{1}{3}\right),e\left(\frac{4}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 5472 }(85, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{72}\right)\) | \(i\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{47}{72}\right)\) |