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 \(\chi_{2793}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5586.el
\(\chi_{5586}(29,\cdot)\) \(\chi_{5586}(71,\cdot)\) \(\chi_{5586}(155,\cdot)\) \(\chi_{5586}(281,\cdot)\) \(\chi_{5586}(659,\cdot)\) \(\chi_{5586}(743,\cdot)\) \(\chi_{5586}(827,\cdot)\) \(\chi_{5586}(869,\cdot)\) \(\chi_{5586}(953,\cdot)\) \(\chi_{5586}(1457,\cdot)\) \(\chi_{5586}(1541,\cdot)\) \(\chi_{5586}(1625,\cdot)\) \(\chi_{5586}(1751,\cdot)\) \(\chi_{5586}(1877,\cdot)\) \(\chi_{5586}(2339,\cdot)\) \(\chi_{5586}(2423,\cdot)\) \(\chi_{5586}(2465,\cdot)\) \(\chi_{5586}(2675,\cdot)\) \(\chi_{5586}(3053,\cdot)\) \(\chi_{5586}(3221,\cdot)\) \(\chi_{5586}(3263,\cdot)\) \(\chi_{5586}(3347,\cdot)\) \(\chi_{5586}(3473,\cdot)\) \(\chi_{5586}(3851,\cdot)\) \(\chi_{5586}(3935,\cdot)\) \(\chi_{5586}(4061,\cdot)\) \(\chi_{5586}(4145,\cdot)\) \(\chi_{5586}(4271,\cdot)\) \(\chi_{5586}(4649,\cdot)\) \(\chi_{5586}(4733,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3725,4903,4999)\) → \((-1,e\left(\frac{3}{7}\right),e\left(\frac{17}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 5586 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{13}{63}\right)\) |