Basic properties
Modulus: | \(8001\) | |
Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | 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 8001.mf
\(\chi_{8001}(104,\cdot)\) \(\chi_{8001}(209,\cdot)\) \(\chi_{8001}(272,\cdot)\) \(\chi_{8001}(398,\cdot)\) \(\chi_{8001}(797,\cdot)\) \(\chi_{8001}(1154,\cdot)\) \(\chi_{8001}(1217,\cdot)\) \(\chi_{8001}(1301,\cdot)\) \(\chi_{8001}(1406,\cdot)\) \(\chi_{8001}(1427,\cdot)\) \(\chi_{8001}(1469,\cdot)\) \(\chi_{8001}(1847,\cdot)\) \(\chi_{8001}(1931,\cdot)\) \(\chi_{8001}(3002,\cdot)\) \(\chi_{8001}(3254,\cdot)\) \(\chi_{8001}(3317,\cdot)\) \(\chi_{8001}(3569,\cdot)\) \(\chi_{8001}(4262,\cdot)\) \(\chi_{8001}(4367,\cdot)\) \(\chi_{8001}(4388,\cdot)\) \(\chi_{8001}(4997,\cdot)\) \(\chi_{8001}(5249,\cdot)\) \(\chi_{8001}(5375,\cdot)\) \(\chi_{8001}(5396,\cdot)\) \(\chi_{8001}(5585,\cdot)\) \(\chi_{8001}(5648,\cdot)\) \(\chi_{8001}(5963,\cdot)\) \(\chi_{8001}(6005,\cdot)\) \(\chi_{8001}(6089,\cdot)\) \(\chi_{8001}(6194,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{5}{6}\right),-1,e\left(\frac{29}{63}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(104, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{1}{6}\right)\) |