Basic properties
| Modulus: | \(16900\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(260\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4225}(512,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16900.fi
\(\chi_{16900}(73,\cdot)\) \(\chi_{16900}(317,\cdot)\) \(\chi_{16900}(333,\cdot)\) \(\chi_{16900}(837,\cdot)\) \(\chi_{16900}(853,\cdot)\) \(\chi_{16900}(1097,\cdot)\) \(\chi_{16900}(1373,\cdot)\) \(\chi_{16900}(1617,\cdot)\) \(\chi_{16900}(1633,\cdot)\) \(\chi_{16900}(1877,\cdot)\) \(\chi_{16900}(2137,\cdot)\) \(\chi_{16900}(2153,\cdot)\) \(\chi_{16900}(2397,\cdot)\) \(\chi_{16900}(2413,\cdot)\) \(\chi_{16900}(2673,\cdot)\) \(\chi_{16900}(2917,\cdot)\) \(\chi_{16900}(2933,\cdot)\) \(\chi_{16900}(3177,\cdot)\) \(\chi_{16900}(3437,\cdot)\) \(\chi_{16900}(3453,\cdot)\) \(\chi_{16900}(3697,\cdot)\) \(\chi_{16900}(3713,\cdot)\) \(\chi_{16900}(3973,\cdot)\) \(\chi_{16900}(4217,\cdot)\) \(\chi_{16900}(4233,\cdot)\) \(\chi_{16900}(4477,\cdot)\) \(\chi_{16900}(4737,\cdot)\) \(\chi_{16900}(4753,\cdot)\) \(\chi_{16900}(4997,\cdot)\) \(\chi_{16900}(5013,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{260})$ |
| Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((8451,677,12001)\) → \((1,e\left(\frac{9}{20}\right),e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 16900 }(4737, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{260}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{37}{260}\right)\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{189}{260}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{237}{260}\right)\) | \(e\left(\frac{27}{130}\right)\) |