Basic properties
| Modulus: | \(206400\) | |
| Conductor: | \(68800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1680\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{68800}(91,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 206400.brm
\(\chi_{206400}(91,\cdot)\) \(\chi_{206400}(331,\cdot)\) \(\chi_{206400}(571,\cdot)\) \(\chi_{206400}(691,\cdot)\) \(\chi_{206400}(931,\cdot)\) \(\chi_{206400}(1531,\cdot)\) \(\chi_{206400}(2011,\cdot)\) \(\chi_{206400}(3211,\cdot)\) \(\chi_{206400}(3331,\cdot)\) \(\chi_{206400}(3931,\cdot)\) \(\chi_{206400}(4291,\cdot)\) \(\chi_{206400}(5491,\cdot)\) \(\chi_{206400}(5731,\cdot)\) \(\chi_{206400}(6091,\cdot)\) \(\chi_{206400}(6211,\cdot)\) \(\chi_{206400}(6691,\cdot)\) \(\chi_{206400}(7171,\cdot)\) \(\chi_{206400}(8371,\cdot)\) \(\chi_{206400}(8491,\cdot)\) \(\chi_{206400}(9091,\cdot)\) \(\chi_{206400}(10411,\cdot)\) \(\chi_{206400}(10891,\cdot)\) \(\chi_{206400}(11011,\cdot)\) \(\chi_{206400}(11371,\cdot)\) \(\chi_{206400}(12331,\cdot)\) \(\chi_{206400}(13531,\cdot)\) \(\chi_{206400}(14611,\cdot)\) \(\chi_{206400}(15571,\cdot)\) \(\chi_{206400}(15811,\cdot)\) \(\chi_{206400}(16171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1680})$ |
| Fixed field: | Number field defined by a degree 1680 polynomial (not computed) |
Values on generators
\((148351,116101,68801,173377,76801)\) → \((-1,e\left(\frac{9}{16}\right),1,e\left(\frac{1}{5}\right),e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 206400 }(91, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{207}{560}\right)\) | \(e\left(\frac{479}{1680}\right)\) | \(e\left(\frac{407}{420}\right)\) | \(e\left(\frac{583}{1680}\right)\) | \(e\left(\frac{83}{840}\right)\) | \(e\left(\frac{1667}{1680}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{7}{240}\right)\) | \(e\left(\frac{69}{280}\right)\) |