Basic properties
Modulus: | \(8640\) | |
Conductor: | \(4320\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4320}(1757,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.hg
\(\chi_{8640}(137,\cdot)\) \(\chi_{8640}(473,\cdot)\) \(\chi_{8640}(617,\cdot)\) \(\chi_{8640}(1433,\cdot)\) \(\chi_{8640}(1577,\cdot)\) \(\chi_{8640}(1913,\cdot)\) \(\chi_{8640}(2057,\cdot)\) \(\chi_{8640}(2873,\cdot)\) \(\chi_{8640}(3017,\cdot)\) \(\chi_{8640}(3353,\cdot)\) \(\chi_{8640}(3497,\cdot)\) \(\chi_{8640}(4313,\cdot)\) \(\chi_{8640}(4457,\cdot)\) \(\chi_{8640}(4793,\cdot)\) \(\chi_{8640}(4937,\cdot)\) \(\chi_{8640}(5753,\cdot)\) \(\chi_{8640}(5897,\cdot)\) \(\chi_{8640}(6233,\cdot)\) \(\chi_{8640}(6377,\cdot)\) \(\chi_{8640}(7193,\cdot)\) \(\chi_{8640}(7337,\cdot)\) \(\chi_{8640}(7673,\cdot)\) \(\chi_{8640}(7817,\cdot)\) \(\chi_{8640}(8633,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,6401,3457)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{1}{18}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8640 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{7}{36}\right)\) |