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 \(\chi_{4320}(3787,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8640.hn
\(\chi_{8640}(7,\cdot)\) \(\chi_{8640}(823,\cdot)\) \(\chi_{8640}(967,\cdot)\) \(\chi_{8640}(1303,\cdot)\) \(\chi_{8640}(1447,\cdot)\) \(\chi_{8640}(2263,\cdot)\) \(\chi_{8640}(2407,\cdot)\) \(\chi_{8640}(2743,\cdot)\) \(\chi_{8640}(2887,\cdot)\) \(\chi_{8640}(3703,\cdot)\) \(\chi_{8640}(3847,\cdot)\) \(\chi_{8640}(4183,\cdot)\) \(\chi_{8640}(4327,\cdot)\) \(\chi_{8640}(5143,\cdot)\) \(\chi_{8640}(5287,\cdot)\) \(\chi_{8640}(5623,\cdot)\) \(\chi_{8640}(5767,\cdot)\) \(\chi_{8640}(6583,\cdot)\) \(\chi_{8640}(6727,\cdot)\) \(\chi_{8640}(7063,\cdot)\) \(\chi_{8640}(7207,\cdot)\) \(\chi_{8640}(8023,\cdot)\) \(\chi_{8640}(8167,\cdot)\) \(\chi_{8640}(8503,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,6401,3457)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{8}{9}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8640 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{31}{36}\right)\) |