Basic properties
Modulus: | \(338130\) | |
Conductor: | \(33813\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(816\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{33813}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bvt
\(\chi_{338130}(31,\cdot)\) \(\chi_{338130}(2101,\cdot)\) \(\chi_{338130}(3271,\cdot)\) \(\chi_{338130}(3541,\cdot)\) \(\chi_{338130}(3661,\cdot)\) \(\chi_{338130}(7441,\cdot)\) \(\chi_{338130}(10291,\cdot)\) \(\chi_{338130}(10951,\cdot)\) \(\chi_{338130}(13291,\cdot)\) \(\chi_{338130}(14071,\cdot)\) \(\chi_{338130}(14971,\cdot)\) \(\chi_{338130}(15361,\cdot)\) \(\chi_{338130}(16531,\cdot)\) \(\chi_{338130}(16801,\cdot)\) \(\chi_{338130}(17581,\cdot)\) \(\chi_{338130}(19921,\cdot)\) \(\chi_{338130}(21991,\cdot)\) \(\chi_{338130}(23161,\cdot)\) \(\chi_{338130}(23431,\cdot)\) \(\chi_{338130}(23551,\cdot)\) \(\chi_{338130}(27331,\cdot)\) \(\chi_{338130}(28231,\cdot)\) \(\chi_{338130}(30181,\cdot)\) \(\chi_{338130}(30841,\cdot)\) \(\chi_{338130}(33181,\cdot)\) \(\chi_{338130}(33961,\cdot)\) \(\chi_{338130}(34861,\cdot)\) \(\chi_{338130}(35251,\cdot)\) \(\chi_{338130}(36421,\cdot)\) \(\chi_{338130}(36691,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{816})$ |
Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{1}{3}\right),1,-i,e\left(\frac{9}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
\( \chi_{ 338130 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{581}{816}\right)\) | \(e\left(\frac{281}{816}\right)\) | \(e\left(\frac{29}{136}\right)\) | \(e\left(\frac{445}{816}\right)\) | \(e\left(\frac{383}{816}\right)\) | \(e\left(\frac{583}{816}\right)\) | \(e\left(\frac{141}{272}\right)\) | \(e\left(\frac{61}{816}\right)\) | \(e\left(\frac{127}{408}\right)\) | \(e\left(\frac{91}{102}\right)\) |