Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(865,\cdot)\) | 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)
|
Galois orbit 8002.o
\(\chi_{8002}(35,\cdot)\) \(\chi_{8002}(71,\cdot)\) \(\chi_{8002}(405,\cdot)\) \(\chi_{8002}(417,\cdot)\) \(\chi_{8002}(463,\cdot)\) \(\chi_{8002}(501,\cdot)\) \(\chi_{8002}(615,\cdot)\) \(\chi_{8002}(785,\cdot)\) \(\chi_{8002}(865,\cdot)\) \(\chi_{8002}(1013,\cdot)\) \(\chi_{8002}(1023,\cdot)\) \(\chi_{8002}(1095,\cdot)\) \(\chi_{8002}(1219,\cdot)\) \(\chi_{8002}(1225,\cdot)\) \(\chi_{8002}(1385,\cdot)\) \(\chi_{8002}(1535,\cdot)\) \(\chi_{8002}(1823,\cdot)\) \(\chi_{8002}(1913,\cdot)\) \(\chi_{8002}(2131,\cdot)\) \(\chi_{8002}(2163,\cdot)\) \(\chi_{8002}(2485,\cdot)\) \(\chi_{8002}(2499,\cdot)\) \(\chi_{8002}(2539,\cdot)\) \(\chi_{8002}(2567,\cdot)\) \(\chi_{8002}(2655,\cdot)\) \(\chi_{8002}(2855,\cdot)\) \(\chi_{8002}(2859,\cdot)\) \(\chi_{8002}(2865,\cdot)\) \(\chi_{8002}(2939,\cdot)\) \(\chi_{8002}(3007,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{94}{125}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(865, a) \) | \(1\) | \(1\) | \(e\left(\frac{94}{125}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{57}{125}\right)\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{41}{125}\right)\) | \(e\left(\frac{14}{125}\right)\) | \(e\left(\frac{14}{125}\right)\) | \(e\left(\frac{106}{125}\right)\) | \(e\left(\frac{26}{125}\right)\) |