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.je
\(\chi_{5472}(67,\cdot)\) \(\chi_{5472}(355,\cdot)\) \(\chi_{5472}(763,\cdot)\) \(\chi_{5472}(907,\cdot)\) \(\chi_{5472}(1003,\cdot)\) \(\chi_{5472}(1123,\cdot)\) \(\chi_{5472}(1435,\cdot)\) \(\chi_{5472}(1723,\cdot)\) \(\chi_{5472}(2131,\cdot)\) \(\chi_{5472}(2275,\cdot)\) \(\chi_{5472}(2371,\cdot)\) \(\chi_{5472}(2491,\cdot)\) \(\chi_{5472}(2803,\cdot)\) \(\chi_{5472}(3091,\cdot)\) \(\chi_{5472}(3499,\cdot)\) \(\chi_{5472}(3643,\cdot)\) \(\chi_{5472}(3739,\cdot)\) \(\chi_{5472}(3859,\cdot)\) \(\chi_{5472}(4171,\cdot)\) \(\chi_{5472}(4459,\cdot)\) \(\chi_{5472}(4867,\cdot)\) \(\chi_{5472}(5011,\cdot)\) \(\chi_{5472}(5107,\cdot)\) \(\chi_{5472}(5227,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((4447,2053,1217,3745)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{1}{3}\right),e\left(\frac{17}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 5472 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{72}\right)\) | \(i\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{72}\right)\) |