Basic properties
Modulus: | \(8640\) | |
Conductor: | \(8640\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(144\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 8640.hu
\(\chi_{8640}(187,\cdot)\) \(\chi_{8640}(403,\cdot)\) \(\chi_{8640}(427,\cdot)\) \(\chi_{8640}(643,\cdot)\) \(\chi_{8640}(907,\cdot)\) \(\chi_{8640}(1123,\cdot)\) \(\chi_{8640}(1147,\cdot)\) \(\chi_{8640}(1363,\cdot)\) \(\chi_{8640}(1627,\cdot)\) \(\chi_{8640}(1843,\cdot)\) \(\chi_{8640}(1867,\cdot)\) \(\chi_{8640}(2083,\cdot)\) \(\chi_{8640}(2347,\cdot)\) \(\chi_{8640}(2563,\cdot)\) \(\chi_{8640}(2587,\cdot)\) \(\chi_{8640}(2803,\cdot)\) \(\chi_{8640}(3067,\cdot)\) \(\chi_{8640}(3283,\cdot)\) \(\chi_{8640}(3307,\cdot)\) \(\chi_{8640}(3523,\cdot)\) \(\chi_{8640}(3787,\cdot)\) \(\chi_{8640}(4003,\cdot)\) \(\chi_{8640}(4027,\cdot)\) \(\chi_{8640}(4243,\cdot)\) \(\chi_{8640}(4507,\cdot)\) \(\chi_{8640}(4723,\cdot)\) \(\chi_{8640}(4747,\cdot)\) \(\chi_{8640}(4963,\cdot)\) \(\chi_{8640}(5227,\cdot)\) \(\chi_{8640}(5443,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{144})$ |
Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((2431,3781,6401,3457)\) → \((-1,e\left(\frac{1}{16}\right),e\left(\frac{5}{9}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 8640 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{5}{144}\right)\) | \(e\left(\frac{19}{144}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{23}{72}\right)\) |