Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(1479,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8002.m
\(\chi_{8002}(121,\cdot)\) \(\chi_{8002}(439,\cdot)\) \(\chi_{8002}(627,\cdot)\) \(\chi_{8002}(635,\cdot)\) \(\chi_{8002}(1289,\cdot)\) \(\chi_{8002}(1479,\cdot)\) \(\chi_{8002}(1613,\cdot)\) \(\chi_{8002}(1725,\cdot)\) \(\chi_{8002}(1793,\cdot)\) \(\chi_{8002}(2563,\cdot)\) \(\chi_{8002}(2723,\cdot)\) \(\chi_{8002}(3119,\cdot)\) \(\chi_{8002}(3249,\cdot)\) \(\chi_{8002}(3281,\cdot)\) \(\chi_{8002}(3505,\cdot)\) \(\chi_{8002}(3533,\cdot)\) \(\chi_{8002}(4469,\cdot)\) \(\chi_{8002}(4497,\cdot)\) \(\chi_{8002}(4721,\cdot)\) \(\chi_{8002}(4753,\cdot)\) \(\chi_{8002}(4883,\cdot)\) \(\chi_{8002}(5279,\cdot)\) \(\chi_{8002}(5439,\cdot)\) \(\chi_{8002}(6209,\cdot)\) \(\chi_{8002}(6277,\cdot)\) \(\chi_{8002}(6389,\cdot)\) \(\chi_{8002}(6523,\cdot)\) \(\chi_{8002}(6713,\cdot)\) \(\chi_{8002}(7367,\cdot)\) \(\chi_{8002}(7375,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\(3\) → \(e\left(\frac{73}{80}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(1479, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{80}\right)\) | \(-i\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{77}{80}\right)\) |