Basic properties
Modulus: | \(4320\) | |
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: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4320.fy
\(\chi_{4320}(229,\cdot)\) \(\chi_{4320}(349,\cdot)\) \(\chi_{4320}(589,\cdot)\) \(\chi_{4320}(709,\cdot)\) \(\chi_{4320}(949,\cdot)\) \(\chi_{4320}(1069,\cdot)\) \(\chi_{4320}(1309,\cdot)\) \(\chi_{4320}(1429,\cdot)\) \(\chi_{4320}(1669,\cdot)\) \(\chi_{4320}(1789,\cdot)\) \(\chi_{4320}(2029,\cdot)\) \(\chi_{4320}(2149,\cdot)\) \(\chi_{4320}(2389,\cdot)\) \(\chi_{4320}(2509,\cdot)\) \(\chi_{4320}(2749,\cdot)\) \(\chi_{4320}(2869,\cdot)\) \(\chi_{4320}(3109,\cdot)\) \(\chi_{4320}(3229,\cdot)\) \(\chi_{4320}(3469,\cdot)\) \(\chi_{4320}(3589,\cdot)\) \(\chi_{4320}(3829,\cdot)\) \(\chi_{4320}(3949,\cdot)\) \(\chi_{4320}(4189,\cdot)\) \(\chi_{4320}(4309,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((2431,3781,2081,3457)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{5}{9}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4320 }(349, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{25}{36}\right)\) |