Basic properties
Modulus: | \(5472\) | |
Conductor: | \(5472\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.js
\(\chi_{5472}(211,\cdot)\) \(\chi_{5472}(547,\cdot)\) \(\chi_{5472}(979,\cdot)\) \(\chi_{5472}(1219,\cdot)\) \(\chi_{5472}(1267,\cdot)\) \(\chi_{5472}(1363,\cdot)\) \(\chi_{5472}(1579,\cdot)\) \(\chi_{5472}(1915,\cdot)\) \(\chi_{5472}(2347,\cdot)\) \(\chi_{5472}(2587,\cdot)\) \(\chi_{5472}(2635,\cdot)\) \(\chi_{5472}(2731,\cdot)\) \(\chi_{5472}(2947,\cdot)\) \(\chi_{5472}(3283,\cdot)\) \(\chi_{5472}(3715,\cdot)\) \(\chi_{5472}(3955,\cdot)\) \(\chi_{5472}(4003,\cdot)\) \(\chi_{5472}(4099,\cdot)\) \(\chi_{5472}(4315,\cdot)\) \(\chi_{5472}(4651,\cdot)\) \(\chi_{5472}(5083,\cdot)\) \(\chi_{5472}(5323,\cdot)\) \(\chi_{5472}(5371,\cdot)\) \(\chi_{5472}(5467,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4447,2053,1217,3745)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{1}{3}\right),e\left(\frac{1}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 5472 }(211, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(1\) | \(e\left(\frac{25}{72}\right)\) |