Basic properties
Modulus: | \(5586\) | |
Conductor: | \(2793\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2793}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5586.eh
\(\chi_{5586}(17,\cdot)\) \(\chi_{5586}(47,\cdot)\) \(\chi_{5586}(593,\cdot)\) \(\chi_{5586}(605,\cdot)\) \(\chi_{5586}(689,\cdot)\) \(\chi_{5586}(845,\cdot)\) \(\chi_{5586}(1013,\cdot)\) \(\chi_{5586}(1487,\cdot)\) \(\chi_{5586}(1613,\cdot)\) \(\chi_{5586}(1643,\cdot)\) \(\chi_{5586}(1811,\cdot)\) \(\chi_{5586}(2189,\cdot)\) \(\chi_{5586}(2201,\cdot)\) \(\chi_{5586}(2411,\cdot)\) \(\chi_{5586}(2441,\cdot)\) \(\chi_{5586}(2609,\cdot)\) \(\chi_{5586}(2987,\cdot)\) \(\chi_{5586}(2999,\cdot)\) \(\chi_{5586}(3083,\cdot)\) \(\chi_{5586}(3209,\cdot)\) \(\chi_{5586}(3239,\cdot)\) \(\chi_{5586}(3407,\cdot)\) \(\chi_{5586}(3785,\cdot)\) \(\chi_{5586}(3797,\cdot)\) \(\chi_{5586}(3881,\cdot)\) \(\chi_{5586}(4007,\cdot)\) \(\chi_{5586}(4205,\cdot)\) \(\chi_{5586}(4583,\cdot)\) \(\chi_{5586}(4595,\cdot)\) \(\chi_{5586}(4679,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3725,4903,4999)\) → \((-1,e\left(\frac{25}{42}\right),e\left(\frac{5}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 5586 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(-1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{41}{63}\right)\) |