Basic properties
Modulus: | \(8018\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4009}(967,\cdot)\) | 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 8018.cz
\(\chi_{8018}(123,\cdot)\) \(\chi_{8018}(199,\cdot)\) \(\chi_{8018}(359,\cdot)\) \(\chi_{8018}(593,\cdot)\) \(\chi_{8018}(777,\cdot)\) \(\chi_{8018}(967,\cdot)\) \(\chi_{8018}(1043,\cdot)\) \(\chi_{8018}(1203,\cdot)\) \(\chi_{8018}(1621,\cdot)\) \(\chi_{8018}(1811,\cdot)\) \(\chi_{8018}(1859,\cdot)\) \(\chi_{8018}(1887,\cdot)\) \(\chi_{8018}(2379,\cdot)\) \(\chi_{8018}(2703,\cdot)\) \(\chi_{8018}(3125,\cdot)\) \(\chi_{8018}(3645,\cdot)\) \(\chi_{8018}(3969,\cdot)\) \(\chi_{8018}(4489,\cdot)\) \(\chi_{8018}(4813,\cdot)\) \(\chi_{8018}(4911,\cdot)\) \(\chi_{8018}(5001,\cdot)\) \(\chi_{8018}(5419,\cdot)\) \(\chi_{8018}(5609,\cdot)\) \(\chi_{8018}(5685,\cdot)\) \(\chi_{8018}(5755,\cdot)\) \(\chi_{8018}(6267,\cdot)\) \(\chi_{8018}(6599,\cdot)\) \(\chi_{8018}(6685,\cdot)\) \(\chi_{8018}(6875,\cdot)\) \(\chi_{8018}(6951,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 8018 }(967, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) |