Basic properties
Modulus: | \(5610\) | |
Conductor: | \(187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{187}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fc
\(\chi_{5610}(61,\cdot)\) \(\chi_{5610}(211,\cdot)\) \(\chi_{5610}(481,\cdot)\) \(\chi_{5610}(541,\cdot)\) \(\chi_{5610}(601,\cdot)\) \(\chi_{5610}(721,\cdot)\) \(\chi_{5610}(811,\cdot)\) \(\chi_{5610}(1051,\cdot)\) \(\chi_{5610}(1201,\cdot)\) \(\chi_{5610}(1261,\cdot)\) \(\chi_{5610}(1591,\cdot)\) \(\chi_{5610}(1711,\cdot)\) \(\chi_{5610}(2131,\cdot)\) \(\chi_{5610}(2251,\cdot)\) \(\chi_{5610}(2521,\cdot)\) \(\chi_{5610}(2581,\cdot)\) \(\chi_{5610}(2791,\cdot)\) \(\chi_{5610}(2851,\cdot)\) \(\chi_{5610}(3031,\cdot)\) \(\chi_{5610}(3121,\cdot)\) \(\chi_{5610}(3241,\cdot)\) \(\chi_{5610}(3361,\cdot)\) \(\chi_{5610}(3781,\cdot)\) \(\chi_{5610}(4111,\cdot)\) \(\chi_{5610}(4171,\cdot)\) \(\chi_{5610}(4561,\cdot)\) \(\chi_{5610}(4681,\cdot)\) \(\chi_{5610}(4771,\cdot)\) \(\chi_{5610}(4831,\cdot)\) \(\chi_{5610}(4891,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((1,1,e\left(\frac{1}{10}\right),e\left(\frac{13}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 5610 }(2851, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{20}\right)\) |